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'0-AIN5 671 RESOURCES CONFUSIONS AND COWTIILITY IN DUAL MCIS /TRACKINO: DISPLAYS CO.. CU) RIR FORCE INST OF TECH
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RESOURCES, CONFUSIONS, AND COMPATIBILITY IN DUAL AXIS TRACKING:DISPLAYS, CONTROLS, AND DYNAMICS
BY
MARTIN LEE FRACKER
B.A., Seattle Pacific University, 1977M.S., Western Washington University, 1981
THESIS
Submitted in partial fulfillment of the requirementsfor the degree of Doctor of Philosophy in Psychology
in the Graduate College of theUniversity of Illinois at Urbana-Champaign, 1987
Urbana, Illinois
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RESOURCES, CONFUSIONS, AND COMPATIBILITY IN DUAL AXIS TRACKING:DISPLAYS, CONTROLS, AND DYNAMICS
Martin Lee Fracker, Ph.D. d,
Department of PsychologyUniversity of Illinois at Urbana-Champaign, 1987
Christopher D. Wickens, Advisor
Dual axis compensatory tracking was investigated as a function
of whether error displays were integrated or separated, whether axis
controls were integrated into one stick or remained separate, and
whether the control dynamics on the two axes were the same or
different. Tracking error increased and control activity decreased
as a function of the summed difficulty of the two control dynamics.
Integrated displays and integrated contr-ols both led to increased
confusions between tracking axes although error was unaffected.
Importantly, performance was also affected by whether the integrality
of displays matched that of controls. These results suggest that
dual axis tracking is subject to separate effects of resource
competition, confusions, and Wickens' compatibility of proximity
principle.
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ACKNOWLEDGEMENTS
Support for the research reported in this paper was provided by
.a contract with the Army Human Engineering Laboratory Contract DAAA
15-86-R-0046. Kathleen Christ was the technical monitor. The views,
opinions, and findings contained in this paper are those of the
author and do not reflect any position, policy, or decision of any
agency within the Department of Defense. The author thanks Roger
Marsh who did the programming and Patricia Martinez who assisted in
the data collection.
5%
46
TABLE OF CONTENTS
Section Page
INTRODUCTION......................................................1
METHOD............................................................ 35
RESULTS . ......................................................... 45 a
D..DISCUSSION ...................................................... 189
REFERENCES ....................................................... 112
VITA............................................................. 130 2,"
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INTRODUCTION
As technology grows ever more complex, there is a danger that
human operators will be pushed beyond the limits of their abilities
to maintain safe and effective system operation. No where is this
danger more evident than in aviation, especially military aviation.
For example, the modern fighter pilot must supervise or control his
aircraft's flight control, navigation, communication, threat
identification, target acquisition, weapons delivery, and electronic
countermeasure systems--all at the same time, perhaps even as his
life is immediately threatened.
Of central concern in aviation is the problem of multi-axis
control. For example, helicopter pilots must guide their vehicle
through all three spatial dimensions of translation and must contend
with the rotational dimension as well. Because all axes of motion
must be controlled simultaneously, aircraft control systems should be
designed to enhance the pilot's ability to control multiple axes at
once. The United States Army has been especially interested in
whether the two hand controllers currently used in helicopters (the
collective and cyclic) should be combined into a single integrated
side-arm controller (Harworth, Bivens, & Shively, 1986; Hemingway,
1984).
Whether multi-axis controls should be integrated into a single
controller may depend upon whether displays for each axis are also
integrated, and whether the control dynamics with respect to each
% %.
2
axis are the same or different. Thus, three primary issues may be
identified: (1) whether the controls for each axis should be
integrated into a single control, (2) whether displays for the
several axes should then also be integrated into a single display
with a single object representing the aircraft's motion in each axis,
and (3) whether the answers to the first two questions depend upon
the control dynamics of the aircraft along each axis.
The purpose of the present paper is to review the existing
psychological literature pertaining to these three issues and to
report the results of a new experiment. Because theory is needed to
generalize beyond experimental findings to applications in practical
settings, the review will evaluate empirical findings from three
theoretical perspectives: attentional resource theory, signal
confusion theory, and Wickens' (1986c) compatibility of proximity '
hypothesis. During the course of the review, it will become clear
that some important questions still remain unanswered, These
questions will provide the background for a new experiment that will
then be reported.
Theoretical Perspectives: '-
Resources, Confusions, and Compatibility
Whether human performance in dual axis tracking is enhanced or -
degraded by various configurations of displays, controls, and control
dynamics is an empirical question. Yet some theoretical perspective
is needed to permit generalization from usually abstract experimental
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tasks to the concrete "real world" tasks of interest. Three
candidates for that perspective are considered here: attentional
resource theory (e.g., Gopher & Navon, 1979; Kahneman, 1973; Navon &
Gopher, 1979; Norman & Bobrow, 1975; Wickens, 1980, 1984a,b,
1987a,b), confusions theory (e.g., Duncan, 1979; Hirst & Kalmar,
1987; Klapp et al., 1985; Levison & Elkind, 1967; Navon & Miller,
1986), and Wickens' (1986c) compatibility of proximity hypothesis.
Attentional Resource Theory
Concepts of a limited attentional capacity began appearing in
the psychological literature during the decade of the 1960's (e.g.,
Chernikoff, Duey, & Taylor, 1960; Moray, 1967). From those early
hypotheses, there developed several sophisticated theories all of
which assumed that task performance could be related to the task's
demand for processing resources (e.g., Friedman, Polson, Dafoe, &
Gaskill, 1982; Kahneman, 1973, Navon & Gopher, 1979; Norman & Bobrow,
1975; Wickens, 1980, 1984b). When multiple tasks are performed
together, therefore, the decrements in their performance should be
predictable from their summed resource demand.
This prediction of resource theory can account for data from a
large number of experiments (for reviews, see Kahneman, 1973; Navon &
Gopher, 1979; Shiffrin & Schneider, 1977; Schneider & Shiffrin, 1977;
Wickens, 1984a,b). Consequently, resource theory has gained
widespread acceptance even though the issue of whether resources
exist is still a matter of discussion in the literature (Gopher,
Y- L "k AA P
4
1986; Hirst & Kalmar, 1987; Navon & Miller, in press; Wickens,
1986a). Further, it should be noted that some capacity theorists
have posited a single resource drawn upon by all tasks (e.g.,
Kahneman, 1973; Kantowitz, 1985) while others have argued for several
independent resources (e.g., Friedman et al., 1982; Navon & Gopher,
1979; Wickens, 1980, 1984a,b). In the present study, however, the
issue of one or multiple resources will not come up and so will not
be addressed.
An issue that will be addressed is an important distinction
proposed here between "strong" and "weak" resource theorists. Both
groups of theorists agree that performance is a function of the
scarcity of resources; the two groups are to be differentiated only
by what they have in mind when they use the term "resources". This
distinction between strong and weak theories is important because, as
will become clear, the conditions sufficient to establish resource
competition are defined differently by the two groups.
Strong resource theorists have followed Kahneman (1973) in
defining a resource as energy to be distinguished from the processing
structures to which such energy might be allocated (e.g., Friedman et
al., 1982; Herdman & Friedman, 1985; Gopher & Navon, 1979; Kantowitz,
1985; Navon & Gopher, 1979; cf., Navon, 1984). Thus, in order to
show that tasks compete for a common pool of energy rather than just
common processing structures, strong theorists maintain that two
conditions must be met. First, it must be the case that the resource
% N N
5
demand of the two tasks together can reasonably be assumed to exceed
the total amount available. Second, instructions to allocate
attention away from one task to another by varying degrees must
result in corresponding changes in how well the two tasks are
performed (cf., Norman & Bobrow, 1975; Wickens, 1984b).
Weak resource or demand theorists, on the other hand, have
followed Norman & Bobrow (1975) in allowing a resource to include the
entire set of processing structures and sources of energy used by a
task or task component. Gopher (1986) was clear in this regard when
he wrote that "the definition of resources as proposed
here...includes both structural and energetical components" (p. 356).
Wickens (1984b) espoused a similar position, when in the context of a
multiple resource model, he defined resources as whatever
"categorical distinctions [between tasks)...account for the greatest
variance in time-sharing efficiency" (p. 91, brackets added), and
again when he observed that "very rapid intertask (or interchannel)
switching may, for all intents and purposes, be labeled as shared
resources" (p. 87).
As a result of their broad definition of the term "resource",
demand theorists are willing to accept a more lenient criterion for
showing that two tasks (or task components) share a common resource.
As with the strong theorists, the assumption that the summed demand
of both tasks exceeds the total supply of a given resource must be
reasonable. But because there is no need to distinguish energy from
".
processing structures, the second condition proposed by the strong
theorists is not regarded as necessary (though it is sufficient).
Instead, demand theorists require only that the quality of
performance in one task can be shown to decrease with the increasing
demand of a loading task.
In the present study, demand theory rather than the strong
version of resource theory is what is examined. Although Kantowitz
(1985) has described demand theory as uninteresting, Navon (1984) has
argued persuasively that energy can not be distinguished empirically
from processing structures after all. Thus, he concludes that strong
resource theory is untestable. Further, demand theory is not
uninteresting if the alternatives to it deny the primacy of demand or
scarcity in multiple task performance. One such alternative has
recently been offered and will now be considered.
Confusion Theory
Navon (1985; Navon & Miller, in press) has proposed that dual
task decrements in performance can be understood entirely without
reference to the demand construct. Instead, he suggests that such
decrements can be accounted for by a variety of lntertask confusions
which he generically labels "outcome conflicts". Further, Navon &
Miller (in press) suggest how outcome conflicts may account for data
from a number of experiments traditionally taken to support demand
theory (e.g., Allport, Antonis, & Reynolds, 1972; Baddely, Grant,
Wright, & Thompson, 1975; Friedman & Polson, 1981; Friedman et al.,
-a - . -. . - % - .- _ .- - .% % %-. %.- %. % % % % % - . -
1982; Treisman & Davies, 1973). Other theorists, such as Hirst and 4
Kalmar (1987), have made similar arguments.
Like Navon, Hirst and Kalmar (1987) offer confusions as an
alternative to resource competition in accounting for decrements in
the simultaneous performance of two tasks. Their basic approach was
to show that dual task interference could arise from an increase in
the similarity between tasks along a variety of different dimensions.
This demonstration, they argued, discredited resource theory as
unparsimonious since the only way resource theory could accomodate a
their data was by postulating a separate resource for each dimension °
of similarity. Further, the fact that interference was directly
linked to similarity implies that confusions underlie interference,
although the confusions themselves may be difficult to document.
Hirst and Kalmar's argument is fundamentally an argument of
reasonableness. Their conclusion is that resource theory is
unreasonable, and therefore should be rejected in favor of a theory
based on confusions. But resource theory may be unreasonable only if
it attempts to account for all task interference effects without
reference to other potential mechanisms of interference. Indeed,
confusions theory may also prove to be unreasonable if it likewise
ignores all other potential underlying mechanisms of interference.
Evidence that confusions theory alone may be inadequate as the sole
mechanism of task interference seems apparent from Navon and Miller
(in press).
'a
Navon and Miller reported the results of two experiments both of
which seemed to document the occurence of outcome conflicts. Both
experiments required subjects to search for one type of target in one
channel and another type of target in a second channel. Subjects'reaction times were significantly delayed when non-targets in one of
the channels were in the same category as targets in the other. But,
as the authors themselves noted about their first experiment,
"although a considerable outcome conflict was certainly demonstrated,
it still does not account for the large single- to dual-task
decrement that has been observed here" (p. 8). The authors
attributed the large dual task decrement to a task switching strategy
employed by subjects to cope with the high difficulty of the tasks
involved, although they offered no evidence for such switching. In
an effort to prevent subjects from adopting such a strategy, the
authors ran a second experiment using much simpler tasks but still
found large dual task decrements with only weak evidence for
confusions.
Although the data reported suggest that confusions can only
partially account for dual task decrements, Navon and Miller come to
the conclusion that confusions can account for dual task decrements
in general without reference to the resource construct. Their
reasoning seems to be that since confusions are known to occur and
resources are not known to exist, it is most parsimonious to assume
that there are other kinds of confusions that do account for the4.
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I
9
entire dual task decrement. Evidence that this is their reasoning is
found in the following excerpt:
There might also be other sources of conflict that were
responsible for some or all of the residual task
interference that was not accounted for by the factors we
manipulated.... It is obvious why such conflict... is
impossible to substantiate definitely in our design, as well
as in most other dual task paradigms: It may occur in all
conditions. (p. 7)
In spite of Navon and Miller's assertions, the results they
report are congruent with resource theory if one allows for the
occurrence of intertask confusions. Once subjects recognize the
occurence of confusions, they may pursue one of two strategies. One
strategy would be to simply let the confusions manifest themselves as
errors. The other would be to attempt to inhibit confusions by
invoking some sort of filtering mechanism. Such a mechanism would be
resource consuming, however. Thus, if two high demand tasks use up
nearly all of the available capacity, there might not be a sufficient
residual available for the filter to work efficiently.
In Javon and Miller's first experiment with the two difficult
tasks, resource competition is high which leaves insufficient
resources available for the filter. Thus, both resource competition
and confusions contribute to the overall decrement. In the second
- . . .. at- ... .. . t .. . .. A %.... .. t-t. t. t . a -(' .
10
experiment with the easier tasks, resource competition is lower so
that the filter is more efficient. As a result, few confusions are
in evidence but there is still a dual task decrement due to the total
demand placed on processing resources by the two tasks and the
filter.
Inclusion of confusions along with resources in a general model
of dual task interference would seem to be an important step forward
and has recently been proposed by Wickens (1986a, 1987a,b; cf.,
Duncan, 1979; Garner & Morton, 1969). Besides enlarging
psychologists' present understanding of complex task performance,
such inclusion would provide an important link to other areas of
psychology where the construct of confusions has traditionally played,%
an important role, especially learning and memory (Anderson, 1974,
1985; Battig, 1968; Birnbaum, 1968; Conrad, 1964; Fracker, 1980;
Glenberg, 1976; Goggin & Martin, 1970; Lintern, in preparation;
Lewis & Anderson, 1976; Martin, 1968; Martin, 1972; Mueller, Gautt, &
Evans, 1974; Osgood, 1949; Pozella & Martin, 1973; Postman, 1975;
Shulman, 1972).
In addition, a well defined model of the role of confusions in
human performance may help to account for data currently inexplicable
by resource theory. For example, multiple resource theory predicts
that multiple task performance should deteriorate as tasks increase
in similarity along certain dimensions (Wickens, 1984b). Yet several
studies have found Just the opposite effect comparing similar and
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dissimilar tapping rhythms (Klapp, 1979, 1981; Klapp, Hill, Tyler,
Martin, Jagacinski, & Jones, 1985), identical and dissimilar control
dynamics in Caal axis tracking (Chernikoff, Duey, & Taylor, 1960),
similar and dissimilar stimulus-response mappings in choice reaction
time (Duncan, 1979), and similar and dissimilar timing parameters in
ballistic hand movements (Kelso, Southard, and Goodman, 1979).
Whether confusions theory could account for these data is
another question. If confusions simply increase with increasing task
similarity as Navou & Miller (1986) suggest, then probably not. But
if confusions are some function of the incompatibility of task
requirements (cf., Chernikoff & Lemay, 1963; Klapp et al., 1985;
Kramer, Wickens, & Donchin, 1985; Wickens, 1987ab), then confusions
may account for such data.
At this point in time, however, such notions are speculative.
Data documenting the occurence of confusions is needed. Only after
confusions have been documented across a wide variety of task
combinations will it be possible to construct a model of when and how
they arise.
Compatibility of Proximity
Transcending issues of both demand and confusions theory,
Wickens' (1986c) compatibility of proximity hypothesis holds that
complex tasks can be located in a multidimensional space where each
dimension represents the "proximity" of specific task elements. For
example, one dimension may reference the degree to which information
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12displays are integrated into a single object or are presented
separately. Another dimension may indicate the degree to which
subjects must integrate the two information sources in order to
select an appropriate response. The essence of the hypothesis is
that the quality of performance will improve as the proximity of task
elements with respect to one dimension tends to match that with
respect to every other dimension.
Wickens' (1986c) has summarized a number of experiments which
have tended to support the compatibility of proximity hypothesis
(Barnett & Wickens, in press; Boles & Wickens, in press; Carswell &
Vickens, in press; Casey & Wickens, 1986; Goettl, Kramer, & Wickens,
1986; Wickens et al., 1985). In addition, he has shown that the
hypothesis provides a framework capable of subsuming work from
earlier theorists (e.g., Garner, 1974; Kahneman & Henik, 1981;
Lappin, 1967; Pomerantz, 1981). He has also shown that the .
hypothesis more precisely defines the limits of phenomena reported by
other researchers. To cite just one example, the hypothesis suggests
that the benefit of integrated object displays discussed by Kahneman
& Henik (1981) may be enhanced if the displayed information must be
integrated, but may be attenuated if the displayed information is to
be treated independently--a prediction verified by Wickens and his
associates (Carswell & Vickens, in press; Casey & Wickens, 1986).
Thus, although the mechanism underlying such compatibility of
proximity effects is unknown, the phenomenon appears to be strongly
"
13
established in the empirical literature.
While compatibility of proximity appears to conceptually
different from notions of resource competition and outcome conflicts,
it may not always be possible to empirically distinguish one
mechanism from the other. One task domain in which such distinctions
apparently can be made is dual axis manual control. It is to this.a
domain that the focus of present paper now turns.
Dual Axis Tracking:
Displays, Controls, and the Heterogeneity of Control Dynamics
Resource demand, confusions, and compatibility seem to represent .?
different mechanisms potentially underlying effects of display,
control, and control order configurations on the quality of tracking ',
performance. The potential contributions (or "predictions") of these
three mechanisms will be discussed in two sections. First,
predictions regarding the heterogeneity of dynamics will be treated.
Then, predictions about the effects of display and of control
integrality will be presented. Both sections will address the logic
underlying the predictions and then will review the dual axis
tracking literature relevant to those predictions. As will be seen,
clear tests distinguishing among the three mechanisms have not yet
appeared in the dual axis tracking literature. 1J.
Because the focus of the present study is on how demand,
confusions, and compatibility contribute to the role of displays,
controls, and dynamics in dual axis tracking, only relevant portions
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of the tracking literature are reviewed. Specifically omitted from
the review are those studies which have addressed the more general
issue of axis independence in dual axis tracking (e.g., Adams & 'p
Webber, 1961; Bilodeau, 1955, 1957; Bilodeau & Bilodeau, 1954;
Ellson, 1947; Gopher & Navon, 1979; Hoppe, 1974; Navon, Gopher,
Chillag, & Spitz, 1984). Nevertheless, the conclusions of the .
present study may have implications for the general question of axis i
independence.
Heterogeneity of Control Dynamics
Predictions. When the control dynamics differ on the two axes -
of a dual axis tracking task, resource theory suggests that tracking
error should be a function of the total demand imposed by the two
axes together. Suppose, for example, that one group of subjects
tracked with zero order (position control) dynamics on one axis and
second order (acceleration control) dynamics on the other (the
heterogeneous condition), a second group tracked with zero order
dynamics on both axes, and a third group tracked with second order
dynamics on both axes.
Second order tracking is known to be more demanding than zero
order as well as first order (velocity control) tracking as measured
by subjects' open loop gain, effective time delay, remnant, and
subjective workload ratings (Baty, 1971; Kelly, 1968; McRuer & Jex,
1967; Navon & Gopher, 1980; Wickens, 1984a; Wickens, 1986b; Wickens &
Derrick, 1981; Ziegler, 1968). This increased demand seems to result '
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15
from the need to generate phase lead in second order tracking (KcRuer
& Jex, 1967; Wickens, 1986b) which in turn requires subjects to
perceive the acceleration of the error display, a type of perception
for which humans are poorly suited (Wickens, 1984a).
Therefore, according to demand theory, zero order tracking error
should be greater in the heterogeneous dynamics condition, but
tracking error in the second order axis should be greater in the
homogeneous condition (i.e., when paired with another second order
axis). These differences in tracking error ought to be accompanied
by differences in control gain.
Control gain may index the degree of either subject caution or
control effort. If control effort is assumed to be constant within a
given control order, then as subjects become more cautious, their
open loop gain should decrease. Competition from a secondary task
results in such decreases in gain, presumably because of the
increased demand on processing capacity (Baty, 1971; Levison, Elkind,
& Ward, 1971; Watson, 1972; Damos & Wickens, 1980; Wickens, 1976;
Wickens, 1986b; Wickens & Gopher, 1977). Thus, second order gain
should be greater and zero order gain should be less under
heterogeneous dynamics than under homogeneous control dynamics.
Confusions theory, on the other hand, would predict that
tracking error would be greater under heterogeneous dynamics for both
zero and second order control. The reason is that subjects in the
heterogeneous group must generate two incompatible transfer
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functions: one in which they generate lead in response to the second
order axis, and one in which they generate lag in response to the
zero order axis (KcRuer & Jex, 1967; Wickens, 1986b).
In the language of the optimal control model (Levison, 1982),
heterogeneous subjects must maintain two incompatible mental models
of axis control dynamics while homogeneous subjects need maintain
only one model. This incompatibility between mental models (or
atheoretically, between transfer functions) could lead to two
different--but not mutually exclusive--outcomes. First, what might 5,
be called control order confusions may be manifest in the open loop W
transfer functions of the heterogeneous group. Second, heterogeneous
subjects may decrease their open loop gain as they attempt to avoid
such confusions.
The compatibility of proximity hypothesis predicts an
interaction of the heterogeneity of dynamics with both display and
control integrality. Therefore, discussion of those predictions is
deferred to the section on display and control integrality.
Experimental results. Only a handful of studies have reported
data that might test the discrepant predictions of demand and
confusions theory (Chernikoff, Duey, & Taylor, 1960; Chernikoff &
Lemay, 1963; Levison & Elkind, 1966, 1967; Miller, Jagacinski,
Navalade, & Johnson, 1982; Wempe & Baty, 1968). Levison & Elkind
(1966, 1967) showed that control order confusions do indeed occur but
only in one direction: subjects' open loop response to the zero
order axis took on characteristics of the that to the second order ,
axis. Vempe & Baty (1968) showed that tracking transinformation
rates were lower given dissimilar rather than similar control
dynamics. ,.
From the standpoint of the present hypothesis, the two most
cited studies are those of Chernikoff and his colleagues (Chernikoff_ ,
et al., 1960; Chernikoff & Lemay, 1963). Both studies have
demonstrated that both zero and second order tracking error is worse
under heterogeneous conditions; they did not obtain subjects' open
loop describing functions, however. (Chernikoff et al. (1960)
demonstrated the same effect between zero and first order dynamics as
well as between first and second order dynamics.) One may question,"
though, why both zero and second order error would increase if '
control order confusions are asymmetric. Should not error increase -
only in the axis where confusions are evident if such confusions i
.1%
alone accounted for the increase in error?.'
To answer this question, note that such an asymmetry is
unavoidable given that control order confusions occur at all. This
is because a lead generating open loop response to a zero order plant
would still result in an overall stable system (at least up to the
point where the subject's responses began adding to rather than
subtractuni from the error, probably near or perhaps beyond the upper
limit of the input bandwidth; see McRuer, 198; uickens, 1986b); but
a lag generating response (appropriate for a zero order system) to a
18 f
second order plant would quickly cause the overall system to become
unstable. Consequently, if control order confusions are
bi-directional, subjects would have to suppress those from the zero
order to the second order axis. If suppressing such confusions leads
subjects to track more cautiously, then they may attenuate their open
loop gain. Because lead generation in the zero order task and gain
attenuation in the second order task could both lead to increases in
error relative to tracking under homogeneous dynamics, control order
confusions could account for the data of Chernikoff and his
associates.
Even though control order confusions may account for the above
data, it is not clear that the data contradict demand theory. In
both of the Chernikoff studies, relatively simple disturbance
functions were used. In the 1960 study, subjects tracked a single
sinusoid (.032 hz) in the horizontal axis and a single sinusoid (.053
hz) in the vertical axis. As a result, the time courses of the two
errors were easily predictable.
Tracking in the 1963 experiment was only slightly more difficult
where the input to both axes was the sum of two sinusoids (.048 and
.078 hz) although the two axis signals were 90 degrees out of phase.
Further, the authors do not say whether the phases of the two
sinusoids within a signal were varied across trials, leaving the
reader to presume that they were not. Thus, the time courses of
error in both experiments seem to have been easily predictable, and
19
hence easily learned by the subjects (cf., Krendel & McRuer, 1968;
Pew, 1974; Poulton, 1957; Wickens, 1984a).
The use of these simple disturbance functions and the ability of
human subjects to detect and shadow the periodicity in them
(especially at low frequencies; see Pew, 1974) suggests that the
overall demand on subjects' processing resources may have been low.
But Norman and Bobrow (1975) have shown that increased resource
demand can lead to a performance decrement only if total demand
exhausts the resource supply. Since it appears questionable whether
this requirement was met in the Chernikoff studies, those data should
not be taken as a fair test of demand theory.
Finally, at least one study has reported results clearly
inconsistent with confusions theory. Miller, Jagacinski, Navalade,
and Johnson (1982) had subjects perform a single axis compensatory
target acquisition task with two control sticks. In one condition,
both sticks controlled the target's velocity. In another condition,1.
one stick controlled the target's velocity (first order dynamics) and
the other controlled its position (zero order dynamics). The output
of both sticks were combined to control the target's position.
Miller et al. found that target capture times were longer when
both sticks controlled velocity rather than when one stick controlled
velocity and the other position. This result is notable because it
is exactly the opposite of what would be predicted by confusions
theory. While the results clearly contradict confusions theory, they
dFp
2. _,0
*~l- .~ S V ",W WV - - - - ~ .
"i
20
do not offer support for demand theory since the authors claim that
unpublished experiments also found the heterogeneous combination to
be superior to the position-position combination. This result may
reflect Braune and Wickens' (1986) suggestion that zero and first
order dynamics are roughly equivalent in difficulty. Evidently, the
superiority of heterogeneous control in the Miller et al. study
reflects some dimension of performance not captured by either
confusion or demand theory.
In summary, while it seems that control order confusions can and
do occur, it is not clear that they are inevitable. Further, it
remains to be seen whether resource demand needs to be included in
any account of tracking with heterogeneous dynamics.
Integrality of Displays and of Controls
Predictions. Predictions of demand and confusions theory differ
in regard to the main effect of display integrality. (Most versions
of demand theory make no obvious predictions about the effect of
control integrality on performance. However, Friedman & Polson's
(1981) hypothesis of two independent resources corresponding to the
two cerebral hemispheres suggests that performance should be superior
with separated rather than integrated controls. But, as will be
seen, this is the same prediction made by confusions theory.)
According to demand theory, tracking error should increase when
displays are separated rather than integrated. But according to
confusions theory, tracking error should increase with integrated,
%I
-J ; IP ~ XJT rRF:V 1% ,1 N1 WJ XF ; 1V X7 U ILUL Xr , 1.7 M;n A•f nr XAR. . . .
21
not separated, displays.
If separate error displays are given for each axis, then there
may be frequent instances when both error indicators are not
simultaneously within foveal vision. Subjects may then pursue one
of two possible strategies. They may visually scan back. and forth
between axes, looking at the error on one axis and then at the other.
Or they may fixate on some point on the display and observe both
errors simulianeously through peripheral vision.
A scanning strategy may place a load on -.';mory since subjects
must then remember the status of error on a given axis at the time of
the last fixation (cf., Allen, Clements, & Jex, 1970; Onstott, 1976).
Using peripheral vision will avoid loading memory but will load the
perceptual system since perception of the display will then be
relatively degraded due to the lower acuity of peripheral vision.
Either way, demand should increase and, therefore, so should tracking
error (cf., Levison & Elkind, 1967; Levison, Elkind, & Ward, 1971;
Wickens, 1986b).
Confusions theory, on the other hand, holds that tracking error
should be greatest with whatever type of display leads to the most
confusions. Confusions between error signals ought to be greatest
whenever it is most difficult to separate one signal from another,
presumably when both signals are received through a common channel.
If one assumes that visual channels are spatially defined (as in the
spot-light metaphor of attention; cf., Briand & Klein, 1987; Ericksen
o... --. o.. -€- ,, - . - - , . . . ... .- • C . . . . . . . . ..
22
& Yeh, 1985; Kahneman & Treisman, 1984; Posner, 1980; Posner, Snyder,
& Davidson, 1980; Treisman, 1969; Watchel, 196?; Wickens, 1984a),
then confusions should be greatest with integrated rather than
separated displays. Further, Garner's work (Garner, 1974; Garner &
Fefoldy, 1970; cf., Cheng & Pachella, 1984; Pomerantz, 1981) suggeststhat because the dimensions of an integrated cursor (vertical and
horizontal displacement) are integral, a cost in confusions should
arise if the two error signals are uncorrelated.
In addition, if response hands are assumed to define separate
channels within the human motor system (see Kelso, Southard, &
Goodman (1979), Marteniuk & MacKenzie (1980), and Schmidt (1982) for
evidence for and against this view), then confusions should also be
more likely with integrated rather than separated controls. Thus,
confusions theory seems to predict that errors will increase with
both integrated displays and integrated controls while demand theory
predicts Just the opposite for display integrality and is silent on
control integrality.
Other effects could moderate the predictions of confusions
theory. Scanning between axes, for example, might lead to some
confusions given separated displays due to interference effects in
memory (see the discussion of scanning above). Similarly, tracking
with two hands given separated controls could lead to confusions
mediated by incompatible hand movements (Kelso et al., 1979;
Peterson, 1965). In any case, confusions theory predicts that, if
.e
% % % %
'I
23
such confusions can be documented, they will account for whatever
interference effects appear in the tracking error measures. (How
confusions may be documented is described at the end of this
section.)
While demand and confusions theory make different predictions
about display and control main effects, they are silent with respect
to how display and control integrality will combine with the
heterogeneity of dynamics to influence performance. This interaction
is addressed by the compatibility of proximity hypothesis, however.
Specifically, the hypothesis suggests that tracking error will be16
less if displays and controls are both integrated or both separated
than if one is integrated and the other is separated. A process
model of how this interaction between display and control integrality
arises is described next.
Consider first a compensatory dual axis tracking display like
the one shown in Figure 1 where two orthogonal tracking axes define a
two-dimensional plane. In the integrated display, the vertical and
horizontal axes errors are represented by a point in the plane. In
the separated display, the errors are represented by the projections
of this point onto the two axes.
Because the integrated display represents error by means of a
single object, people should have difficulty in separating the two
errors from each other (Carswell & Wickens, in press; Garner, 1974;
Garner & Fefoldy, 1970; Wickens, 1986c; Woods, Wise, & Hanes, 1981).
"", -""" . '"". ,"", ." """. " . """- """. ."" -" "-" % " "%" ,, ", •"• % ' % '," - '.-' " -' . . ."
24
Thus, people may be expected to process the radial error which is
directly represented by the integrated error indicator. With
separate error displays (i.e., the projections of radial error onto
the two axes), on the other hand, subjects should have no trouble in
perceiving the two errors directly.
But now consider the requirements imposed by whether errors on
the two axes are controlled by an integrated control or by two
separated controls. Given separated controls, subjects would need
separate representations of the two errors. Given an integrated
control, subjects could control both errors simultaneously by moving
the control stick at various angles, but this strategy amounts to
controlling radial error and hence requires a radial representation
of error. Consequently, subjects should need a radial representation
of error with an integrated control, and separate representations
given separate controls.
When the needed representation of error is not directly present
in the display, it follows that subjects must generate that
representation themselves. That is, subjects with an integrated
display but separated controls will need somehow to recover the
projections of the radial error onto the vertical and horizontal
axes. Similarly, subjects with separated displays but an integrated
control should find the intersection of the two errors in the dual
axis plane. Both of these processes will be referred to as "mapping
operations".
25
integrated errordisplay
7,,i. I I
".5
radial error "
"4 1 - error reference iI (target)/ 4
separated error ,
displays
Figure 1. Display for a compensatory dual axis tracking task showing !
both separated and integrated error cursors. Also shownis the error reference or target. Radial error refers tothe distance from the error reference to the integratederror cursor; radial errors can also be defined as the"distance between the two separated error cursors. The -figure is a scale representation of the display used in".the present experiment (see Method). '
%-.
k ,, : .. , .. -S,,V ~e .L ... .. .V . ...L ..X .L .L .. ... ... . . .. j ./ -€ , , .. ,., .. ., -, " € ., .. : . ., , . ... ,.- .- ,.: :5 .
26
To the extent that these mapping operations are unsuccessful and
confusions result, tracking error should increase when the
integrality of displays and controls do not match. But tracking
error should also increase to the extent that these mapping
operations are resource demanding and compete with the tracking task
for processing resources. Thus, both confusions and resource demand
may contribute to the same general effect. Further, it should be
possible to distinguish the relative contributions of each under
certain circumstances.
If mapping operations are successful, there should be no
systematic relation between documented confusions and the
compatibility of display and control integrality. But if tracking
error increases in the absence of confusions, then that increase may
be taken as evidence that the mapping operations are resource
demanding. If, on the other hand, confusions are absent and error is
unaffected, then the resource demand of such mapping operations may
be presumed to be minimal.
The latter outcome could also be taken as evidence against the
mapping operation construct, however. Fortunately, it is possible to
validate the existence of mapping operations in the complete absence
of confusion and error effects. From the perspective of mental
chronometry (e.g., Posner, 1978), the mapping operation required when
the integrality of displays and controls do not match should be
detectable as an increase in subjects' effective time delay (cf.,
Lp
I27
Wickens, 1976, 1986). Effective time delay is a control theory
measure of the time it takes subjects to process the error signal
from the moment it has been perceived to the moment of response
execution. (How time delay is computed is described in the Results
section.) In addition, subjects may be more cautious as they carry
out such mapping operations, and this increased caution should appear
as decreases in control gain and control velocity (a measure of the
length of control movements per unit time).
If the operations fail, confusions should appear and be
detectable as signal cross-coherence. Intuitively, cross-coherence
represents control activity in one axis that is linearly related to
error in the opposite axis. More formally, coherence is a measure of
the linear association between two signals within a given bandwidth
and is equivalent to a squared correlation where cases are specific
frequencies and observations are the power in those frequencies for
the two signals (Dixon et al., 1983). (Mathematically, coherence is
the concentration of probability around the least-squares estimate of
the linear transformation that maps one signal onto another within a
given bandwidth. If the bandwidth contains only one measurable
frequency, then the coherence will always be unity.)
Two types of cross-coherence are possible. One, referred to as
primary cross-coherence, indexes confusions between axes; it is the
coherence between the input signal to one axis and the control output
in the other axis. The second type, secondary cross-coherence, is
28
defined only when subjects use separate control sticks which move in
orthogonal directions. Secondary cross-coherence indexes confusions
as to which control stick controls which axis; it is the coherence
between the input signal to one axis and control output in the
correct axis but of the wrong control stick. As such, secondary
cross-coherence does not directly add error to either axis since it
involves control stick displacement along a non-relevant axis.
Besides a display by control integrality interaction, the
compatibility of proximity hypothesis also predicts a more complex
interaction between display and control integrality and the
heterogeneity of dynamics. Specifically, the requirement to adapt to
two distinct tracking dynamics should be more easily met when
displays and controls are both separated than when either or both are
integrated. Similarly, adaptation to the same dynamics on both axes
my be enhanced when displays and controls are both integrated rather
than when one or both are separated. Note that these predictions
imply that displays, controls, and dynamics contribute equally to
compatibility. Whether such equality is the case is an empirical
question, however: it may be that the importance of the three
factors to compatibility are not equal. In any case, incompatible
display-control-dynamics configurations should lead to increased
error due to either an increase in confusions or to the expenditure
of extra effort to avoid confusions.
Experimental results. Unfortunately. few dual axis tracking
I - , , -', :" : " ,, . "- . . , . , ., . ,. ... ,..f .
29
studies have attempted to document confusions by measuring
cross-coherence. Only two studies are known to have collected
cross-coherence data: Damos and Wickens (1980) and Tileman (1979).
Both studies failed to find any significant evidence for confusions,
but both used separated displays and controls. Thus, a serious
attempt to document confusions in dual axis tracking as a function of
display and control integrality is currently lacking in the
literature. Therefore, it is presently possible only to infer the
presence or absence of confusions from other measures such as
tracking error.
As predicted by demand theory, some studies have shown that
separated displays do lead to greater tracking error than do
integrated displays (e.g., Bailey, 1958; Chernikoff & Lemay, 1963;
Sampson & Elkin, 1965). However, Burke, Gilson, and Jagacinski
(1980) found error unaffected by display integrality. One could
argue that the scanning decrement associated with separated displays
was matched by a decrement due to confusions with integrated
displays. But this possibility has yet to be examined.
Although Baty (1971) has provided data suggesting that scanning
is what accounts for the cost to separated displays, Burke et al.'s
study does not seem to have differed from the others in the need for
scanning. But it did differ from Sampson and Elkin's (1965) study in
one important way. While Sampson and Elkin used an integrated
control in all display conditions, Burke et al. used separated
• , , " ,.': " ".€ :- ]P ,¢ ', " "? . ; " ," , ,'. " ."". .."."- ". ".". ".". " . - . " "." '"','0
30
controls. Taken together, these two studies suggest some kind of 'V
interaction between display and control integrality.
Further evidence for a display-control interaction may be found
in a comparison of experiments by Baty (1971), Bartram, BanerJi,
Rothwell, and Smith (1985), and Regan (1960) with one reported by
Levison, Elkind, and Ward (1971). Levison et al. found that tracking
using separated displays was worse with integrated rather than
separated controls. Baty, Bartram et al., and Regan, on the other
hand, found that tracking using integrated displays was better with
an integrated control rather than separated controls.
.e
It is tempting to take these results as rough support for the W
existence of a compatibility of display and control integrality "
effect. Unfortunately, the effect is completely absent in a study
where it ought to be present. Chernikoff and Lemay (1963) had
subjects track in all four conditions needed to test the
compatibility of integrality prediction; that is, the complete
factorial manipulation of display integrality and control N
integrality. They reported no evidence for any interaction whatever
between display and control integrality. '2Although these researchers did not find the predicted
display-control interaction, they did find other evidence favoring p
the compatibility of proximity hypothesis. When control dynamics"I
were the same on both axes, integrated displays led to less tracking
error than did separated displays while control integrality had no
%,
31
effect. But when control dynamics differed between the two axes,
separated controls led to less error than did an integrated control
while display integrality had no effect. -
Although these two interactions conform in a descriptive sense
to the compatibility of proximity hypothesis, the processes which
give rise to them are not entirely clear. Chernikoff and Lemay
suggest that separated displays may help subjects avoid confusions
between control orders but say little beyond this. Concerning
control integrality, they suggest that when heterogeneous dynamics
are used, subjects need separate controls to avoid confusions between
the required "pattern of response movements" (p. 99). But when
homogeneous dynamics are used, confusions between movement patterns
do not occur; hence, separated controls offer no benefit.
This reasoning is not entirely convincing, however. Unless the
two disturbance functions contain the same frequencies and are in
phase with each other, the proper pattern of response movements in
one axis will usually be different from that in the other.
Consequently, confusions should nearly always be possible and ought
to be exacerbated by an integrated control regardless of whether
dynamics are the same or different (bearing in mind that separate
controls may also lead to confusions--see "predictions" above). It
is Just this type of interpretative difficulty that may be alleviated
by documenting the occurrence of axis confusions with cross-coherence
data and control order confusions with a describing function
_.
I32
analysis. IIf Chernikoff and Lemay's data appear problematical, that may be
because of an apparent flaw in their experimental design (besides
their failure to use demanding input signals): the same six subjects
were used in all 12 of the experimental conditions. Since multiples
of 12 subjects are needed to cancel out symmetric carry over effects
in an experiment with 12 conditions, and because no within subjects
design can cancel out asymmetric effects, such effects can not be
ruled out as an explanation for the reported data (cf., Matthews,
1986; Poulton, 1974, 1982; Scheffe, 1959). Consequently, there is a
need to repeat the essentials of their experiment using a between
subjects design so that carry over effects can not account for the
results. The following experiment is intended, in part, to address
this need.
A New Experiment
The present experiment replicates the 12 conditions of the
Chernikoff and Lemay (1963) study but corrects a number of
deficiencies. First, velocity and acceleration control dynamics were
used instead of position and acceleration in order to improve the
relevance of the data to the types of control dynamics typically
found in aviation. Second, the inputs to each axis were the sums of
five sinusoids whose phases were randomly set at the beginning of
each trial in order to make the signals appear random. Third, a
completely randomized between-subjects design was used to eliminate
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33
the concern over carry-over effects. Fourth, single axis tracking
data were collected from all subjects to serve as a baseline for the
dual axis measures. Finally, measures of tracking error were
augmented with several other measures in order to clarify the
contributions of resource demand and confusions to overall
performance. These included measures of control velocity, of
subjects' open loop describing functions, of both primary and
secondary cross-coherence, and of whether subjects adopted serial or
parallel response strategies.
Results of the experiment were expected to clarify the
contributions of resource demand, confusions, and compatibility to
tracking error. Demand theory and confusions theory lead to
incompatible predictions about the effect of the heterogeneity of
dynamics on tracking error; therefore, results of the heterogeneity
manipulation should show clearly whether resource demand or
confusions is the dominant underlying process. Similarly,
contradictory predictions about tracking error are made with respect
to the manipulation of display integrality so that a clear
distinction between confusion and demand processes should again be
possible.
With respect to control integrality as well as the compatibility
of proximity, confusions and resource processes can not be
distinguished on the basis of tracking error alone. In order to
distinguish between them, the logic employed was that tracking error
'e'1
~34
not accounted for by documented confusions should be attributed to
resource demand. It was expected that control integrality would
mainly influence the prevalence of confusions. Further, incompatible
display-control configurations and incompatible proximity of displays
and dual axis tracking dynamics were also expected to lead to
confusions. Demand was expected to be greater under incompatibility
only if subjects made the effort to filter out confusions.
i.
a-
o.
'tt
o4
• ' •W '' '' '' ' ,"" ' •" -' 4 , - - . . * " " " " .°." ... . . . - " " " - - " ".".' .- . . . 0
35
METHOD I
Subjects
All 96 subjects (88 males and 8 females) were right-handed
members of the University of Illinois community who responded to
advertisements in the local community. Most were students majoring
in engineering. Each subject was tested for tracking ability as
described below. Subjects who failed to achieve a satisfactory level
of performance on the test were excluded from participation in the
experiment. Consequently, all 96 subjects in the final sample
possessed a minimum level of tracking ability.
Each subject was paid $3.50 per hour for three hours plus an
hourly bcnus. For most subjects, the hourly bonus amounted to 50
cents.
Task and Stimuli
The dual axis tracking task was constructed out of two,
completely independent single axis compensatory tracking tasks. One
tracking task took place in the vertical dimension and one in the
horizontal. Thus, the dual axis tracking display consisted of a
two-dimensional plane. Whether each axis had its own error cursor or
the two shared a common, integrated cursor was one of the -
experimental variables.
Disturbance inputs. Both disturbance functions were the sum of
five digitally created sinusoids. Each function was consistently
assigned to the horizontal or vertical axes across subjects and :%
- .%
36
conditions. For the horizontal axis, the five input frequencies were
.1304, .2222, .3750, .6383, and 1.1111 hz. For the vertical axis,
the five input frequencies were .1705, .2885, .4918, .8333, and
1.4286 hz.
Care was taken to ensure that, among these ten frequencies,
none was an harmonic of another. Further, the logarithmic distance
between frequencies was maximized within the range of .1304 to 1.4286
hz since the set of ten frequencies were evenly spaced on the
logarithmic scale. Spectral analysis recovered the five frequencies
for both inputs and showed no evidence of "smearing" or of unwanted
spikes at non-input frequencies. The recovered frequencies are
displayed in Figure 2.
For both axes, the first three sinusoids with the slowest
frequencies had gains of 1.0 while the two high-frequency sinusoids
had gains of 0.2. As a result, the contribution of the two highest
frequencies to the overall disturbance function was less than that of
the three lowest frequencies.
Each disturbance function was calculated prior to the start of
each trial. In order to prevent the function from becoming
predictable, the phase (i.e.,-starting point) of each sinusoid was
varied randomly from one trial to another. Since the selection of
phases for the ten sinusoids were independent of each other, the
result was a completely new pair of disturbance signals for every
trial.
"I I
37 1W K, _V N j '
$=SIGNAL X I
+=SIGNAL Y 1
.4 2 4
FREQUENCY (HERTZ)
Figure 2. X and Y axis input signals as recovered by spectral
analysis. Each signal was the sum of 5 sinusoids. Asshown, the frequencies represented in signal X were locatedIin between frequencies represented in signal Y. Note also
that the power in the two upper frequencies of each signalwas about one-fifth that of the three lower frequencies (theordinate of the plot is in log scale units).
% %
IN"~ ~ ~ ~ %11aM1V ak VL1_L11T W W _i1 - * 4 N- -
38
System dynamics. Two different system control dynamics of pure
orders were used: velocity control (first order) and acceleration
control (second order). To achieve velocity control, the output
signal from the subject's control stick was integrated once before
being added to the disturbance signal. To achieve acceleration
control, the output signal was integrated twice and then added to the
disturbance signal.
Control sticks. Subjects attempted to null vertical and
horizontal errors using either separate Joysticks for each axis or a
single, integrated Joystick for both. In either case, vertical
movement of the Joystick controlled the vertical error cursor
("forward" moved the cursor "up") and horizontal movement controlled
the horizontal error cursor. In those conditions in which separate
Joysticks were used for each axis, which stick controlled the
vertical axis and which controlled the horizontal axis was balanced
across subjects.
Compensatory tracking display. The same 190 by 190 pixel (13.4
by 13.4 cm) two-dimensional tracking display was used for both dual
and single axis tasks (see figure 1). The display was outlined with
a yellow box with the zero-error reference indicator placed in the
exact center of the box. A small red cross (.5 by .5 cm) in the
center of the display served as the reference from which all errors
were measured. In the dual axis task, the integrated error cursor
consisted of a larger green "plus sign" (.9 by .9 cm) that moved in
- ~ ~ ~ ~ ~ L.4 L'. -I4 - . ~ .
39
both dimensions simultaneously.
The separated cursors consisted of the vertical and horizontal
bars of the plus sign. Each bar moved along its own axis only: the
vertical bar moved along the horizontal axis and the horizontal bar
moved along the vertical axis. For the single axis task, only the
relevant error cursor was displayed.
Design
A completely randomized between-subjects design was used in
order to avoid transfer effects across conditions. The design
consisted of twelve dual axis conditions formed by the factorial
combination of three variables: display integrality, control
integrality, and heterogeneity of control dynamics.
The display and control integrality manipulations were described
in the preceding paragraphs. Manipulation of heterogeneity of
control dynamics led to three conditions: velocity control on both
axes, acceleration control on both axes, and acceleration control on
one axis and velocity control on the other. Which axis received
which control order was balanced within each relevant condition.
Procedure
Subjects reported to the laboratory for three experimental
sessions. The first session served to introduce subjects to the
experiment and to screen out those individuals who were unable to
perform the dual axis tracking task. Session two was a practice
session and was identical to session three except that data were not
S
DO
40
recorded. Session three was the focus of the experiment. All
reported data were collected in this session. In addition, the
calculation of subject's payment bonuses was based on their
performance in the third session.
Session one: Subject screening. All subjects performed eight
single axis trials and six dual axis trials in session one. All
eight single axis trials (4 vertical and 4 horizontal) were performed
with acceleration control. Likewise, the first four dual axis trials
were performed with acceleration control on both axes. In all
instances, display and control integrality conditions were identical
to those which the subject would experience in sessions two and
three.
At the end of the fourth dual axis trial, a decision was made to
either retain the subject in the experiment or to terminate the
subject's participation. The decision was based solely on whether
the subject had been able to retain control over vertical and
horizontal axis errors in any of the dual axis trials. To facilitate
this decision, a criterion of an average radial error of 1.0 was
adopted where the largest radial error possible was 1.414. Radial
error is the square root of the sum of the squared vertical and
horizontal errors.
The purpose of this screening procedure was to ensure that
subjects admitted into the velocity control conditions were roughly
comparable in tracking ability to those in the more difficult
41
acceleration control conditions. Since acceleration control subjects
had to be able to maintain control over tracking errors in order to
generate meaningful time histories, acceleration control was thought
to provide a more appropriate screening task than does the more
commonly used critical tracking task (e.g., Miller et al., 1982).
Subjects who failed to meet the radial error criterion were
thanked for their participation, given a kind smile, and paid.
Subjects who met the criterion then performed two additional trials
under the system dynamics they would experience in the rest of the
experiment. These subjects were not paid until after the third
session. Further, since their bonus was to be based on third session
performance (a fact not revealed to the subjects), they were not told
the status of their bonus.
Subjects were encouraged to minimize tracking error in two ways.
In addition to the possibility of earning bonuses for small tracking
errors, subjects were always informed of the lowest errors anyone had
achieved in the experiment so far with the same tracking dynamics.
(Records were not reported for individual display-control
configurations as this could have resulted in different perceived
standards among the 12 conditions.) In the dual axis task, the
records reported were for radial error. Several subjects indicated
that these record low errors were highly motivating.
Sessions two and three. As indicated, sessions two and three
were procedurally identical. Subjects first performed a single axis
401
3%
42
trial, then two dual axis trials, followed by another single axis
trial and then two more dual axis trials, and so on for a total of 12
trials. Whether a single vertical or horizontal axis task came first
was balanced within each condition.
Throughout each session, the subject sat in a sound and light
attenuated booth wearing a set of headphones. All communication
between subject and experimenter were via the headphones and a
microphone located in the booth out of the subject's line of sight.
The experimenter began each trial by announcing the type of
trial to be performed (dual, single-vertical, or single-horizontal),
and then asking the subject if he/she was ready. The trial began as
soon as the subject responded "ready". Each trial lasted 120 sec.
At the end of the trial, the experimenter reported to the subject his
or her average horizontal, vertical, and radial axis errors for dual
axis trials and as appropriate for single axis trials. The subject
was then told what the record low error was up to that time for the
type of trial just completed; this message was usually given only
once during each session, following the first appropriate trial. The
next trial began approximately one minute later. No breaks were
otherwise permitted between trials.
Data were collected in the third session only.
Data collected. Two types of data were collected. First,
summary data were collected for every trial. Summary data consisted
of root mean squared observations of tracking error on the vertical,
V.
43
horizontal, and radial axes, and of control stick movement velocity
in both axes. %
Second, time series data were collected for the third horizontal r
and third vertical single axis trials, and for the fourth and sixth
dual axis trials. These time series data consisted of five
observations per second of the value of eight variables in dual axis
trials: the input signal for each axis, the magnitude of displayed
error for each axis, and the position of each control stick in the
horizontal and vertical axes. Of course, only four of these
variables were recorded in single axis trials. These data became the
basis for a control theory analysis of each subject's performance.
Assignment to Conditions
Subjects were assigned to the 12 experimental conditions at
random with the restriction that all conditions would have an equal
number of subjects after every twelfth subject. This assignment
strategy helped assure that temporal changes in the available pool of'°5
subjects would be represented in each condition.
Apparatus
The experiment was under the control of an IBM Personal
Computer running at 4.77 Mhz and updating the tracking display 30
times a second. The display itself was generated on a Princeton
Graphics HX-12 color mnitor. Subjects's hand controls consisted of
two Measurement Systems, Inc. Model 542 Joysticks interfaced with the '
computer via TecMar LabMaster 12-bit A/D inputs. These analog
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44
Joysticks were spring loaded with 360 deg of action available.
Deflections of the joystick were measured with a resolution of 1/1000
of the total nnvei~nt radius.
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45
RESULTS
Before presenting the results of the experiment, it will be
helpful to first define clearly the data that were analyzed. These
data were not the time-series observations themselves but certain
useful transformations of those observations. Then, certain features
of the data analysis approach will be explained in order to enhance
the reader's understanding of what was done. Finally, the adequacy
of the single axis data as a baseline against which to compare the
dual axis measures will be evaluated.
Data Analyzed
Four types of data were analyzed: root mean squared tracking
errors, average control stick velocity, control theory parameters
(including remnant and dual axis cross-coherence), and response
strategy indicators. Root mean square tracking error (rse) is the
square root of the sum of squared tracking errors which were measured
every 200 ms. Control stick velocity was measured as the average
absolute difference in deflection in the control stick between
measures of control stick position; like tracking error, control
stick velocity was also a root mean square measure.
Six control theory parameters were derived: phase intercept,
effective time delay (i.e., phase slope), gain intercept, gain
slope, primary cross-coherence, and secondary cross-coherence. The
derivation of these six parameters was as follows.
First, the entire 120 sec time history for a given trial from a
V % %
46
given subject was subjected to a Fourier transform. This transform
maps the time history data onto the frequency domain and recovers the
sinusoids present in each particular signal. Then, two types of
cross-spectra were calculated within bandwidths of .0167 hz centered
at the five input frequencies: the cross-spectrum between the input
signal and control stick movement, and the cross-spectrum between the
input signal and the displayed error. For convenience, these
cross-spectra will be said to be collected at the bandwidth's center
frequency, the input sinusoid. Thus, separate cross-spectra were
obtained for each of the five sinusoids in the input signal. The
subject's empirical open loop transfer function (see Wickens, 1986)
was determined by dividing the stick cross-spectrum by the error
cross-spectrum for each sinusoid. (Complete mathematical
descriptions of subjects' transfer functions were not obtained.)
Since cross-spectra are represented as complex numbers, the
ratio of two cross-spectra is also a complex number and so may be
represented as a vector in the complex plane. This vector is
completely described by its length and its angle of rotation from the
positive real axis. In control theory terminology, the angle of
rotation is referred to as a phase lag since it measures how far the
subject lags behind the input sinusoid, and the vector length is
referred to as a gain since it measures the ratio of the subject's
gain to the signal's gain.
The phase data were calculated in radians. Phase was found to
'r -r p- - d,_P -A -u
47
be a linear function of frequency when the input frequencies are also
expressed in radians rather than hertz. The slope of the regression
of phase on frequency was taken as the subject's internal time delay
in which he or she was preparing the next sequence of motor movements
(McRuer & Jex, 1967). The intercept of the regression was positive
if subjects were anticipating the input signal but negative if they
were following the signal.
With respect to the gain data, it was possible to obtain a
linear relation between gain and input frequency by taking the
logarithm of both. The common logarithm of gain was then multiplied
by 20 so that gain was expressed in decibels (dB), and 1.0 was added
to the common logarithm of the input frequency (expressed in hertz)
to force the gain intercept to be calculated at 0.10 hz. Because the
gain function was linear in the current data (a condition which is
not true across all frequencies or dynamics), the gain intercept
served as an index of the subject's overall gain while the gain slope
reflected the degree to which the subject changed his or her gain at
higher frequencies. The magnitude and direction of this slope are
diagnostic of the subject's response to the system control dynamics:
a slope of zero dB per decade (of the common log of the input
frequency expressed in hertz) would suggest a zero order (position
control) open loop response to a first order system while a slope of
20 dB per decade would suggest a minus first order (differentiating
or "lead generating") response to a second order system.
I...
48
As stated, linear relations between gain and log frequency and
between phase and frequency were found. In both the first and second
order single axis tasks, the correlations between gain (in dB) and
log sinusoid frequency were .92. Similarly, the correlations between
phase and sinusoid frequency were .97 for both single axis tasks. In
the dual axis tasks, the phase-frequency correlations declined to .90
and the gain-log frequency correlations declined to .80.
Two types of cross-coherence data were also collected. Both
types of cross-coherence were computed for bandwidths of .0167 hz
centered at the five input sinusoids and then averaged across
bandwidths in order to increase their overall reliability (cf.,
Dunlap, Silver, & Bittner, 1986). The first type of cross-coherence
measured was the coherence between the input signal to one axis and00
control stick movements in the other axis; this type is referred to
as primary cross-coherence. A second type, referred to as secondary
cross-coherence, is defined only when subjects used two control
sticks, one stick for each axis. Secondary cross-coherence is the
coherence between an input signal for a given axis and movements of
the wrong stick in that axis.
Two dual axis response strategy indicators were derived for each
subject. One measured the subject's tendency to alternate control
between axes, and the other measured the subject's bias toward one
axis or another. Both measures were determined by examining the 600
observations for each subject on the sixth dual axis trial. First,
-- "4
.%
49 V
counts were obtained for three types of events: (1) the vertical
axis control was off center but the horizontal control was on center
(y-alone), (2) the horizontal control was off center but the vertical
control was on center (x-alone), and (3) both controls were off
center at the same time (both). The x-alone and y-alone counts were
then converted to proportions by dividing them by the sum of the
three counts (i.e., the total number of observations on which the
subject had moved at least one control off center).
Next, the converted x-alone and y-alone measures were
represented by a vector in an x,y plane. The origin of the plane may
be conceptualized as the point representing a pure parallel control
strategy since both controls must always be off center simultaneously
if the x-alone and y-alone measures are both zero. Consequently, the
length of the obtained vector for any subject represents the
"distance" of that subject's response strategy from a pure
simultaneous control strategy. Given a vector of length greater than
zero, the angle of the vector represents the subject's bias toward
one or the other axes. If there were no bias, the angle of the
vector would be 45 degrees. Therefore, the bias measure was simply
the angle of the vector in degrees minus 45. Thus, a positive bias
measure means subjects controlled in the y-axis more than in the
x-axis.
A possible objection to the response strategy measures just
described is that they do not take into account the fact that the x-
and y-axis controls will normally pass through the origin of the'-
control plane at different times even when subjects are engaging in a
pure parallel response strategy, One might argue then that the
strategy vector might be artificially lengthened as a result. This
difficulty can probably be discounted, however, because the position
of either control is measured on an essentially continuous scale
(having 2000 possible values from -1000 to 1000). As a result, the
probability that a continually moving control will be exactly
centered at the time its position is measured is virtually zero.
Other ways of determining whether subjects controlled both axes
serially or in parallel are, of course, possible. For example,
control velocity could have been measured instead of control
position. Then parallel responses could have been defined as
non-zero velocities on both axes simultaneously. Such a procedure
would have been more complicated and would seem to be unnecessary.
Because control position always translated into changes in error
velocity or acceleration, subjects were unlikely to neglect an axis
by holding the control stick off center but at some constant
position. Such an event in a given axis could cause the error to
change at a constant velocity or acceleration, thus causing the
subject to lose control of the error in that axis. (Nomentary holds
might occur during the course of a "bang-bang" response to a second
order system, but they would not indicate neglect.) Thus, using
control position as the criterion for determining response strategy
IV'I
51
seems to be reasonable given the control dynamics under study.
Another possibility would be to have established some small
range of movement in control stick position that was considered
essentially zero for purposes of this analysis. This approach would
allow for noise in the signal from the control stick and so might
increase the sensitivity of the analysis. The control sticks used in
this experiment were of a very high quality, however, and were
virtually noiseless (as determined by running several trials and
measuring control stick position without a subject in the subject
booth). Further, subjects varied widely in how much they deflected
the control stick, and it was feared that defining any small range of
movement as essentially zero would lead to false "detections" of no
movement for those subjects who generally employed small deflections.
Thus, using the criterion of absolutely zero stick deflection seemed
to be both a reasonable and a conservative approach to measuring
subjects' response strategies.
Finally, it should be noted that the x- and y-axes were treated
somewhat differently for subjects in the dynamic heterogeneity
conditions. For subjects in the two homogeneous conditions, the x-
and y-axes represent the horizontal and vertical control axes,
respectively, as would normally be the case. But for subjects in the
heterogeneous condition, this mapping is inappropriate since half the
subjects had first order dynamics and half had second order dynamics
on the horizontal axis. Therefore, the x- and y-axes were
,-
52
arbitrarily redefined so that the first order axis was labeled as x,
and the second order axis was labeled as y. As a result, the
strategy bias parameter represents bias towards a control order for
subjects in the heterogeneity conditions.
Analytic Approach
Prior to analyzing the various measures discussed above, two
important decisions were made. First, it was decided to compare the -
various measures (except the strategy measures) within the first and -
second order axes separately. That is, instead of including the
first and second order homogeneous dynamics conditions in the same
analysis, they were each included in separate analyses. In one -
analysis, then, first order tracking when both axes were first order
was compared to first order tracking when the other task was second
order. An identical analysis was then conducted for second order a
tracking.
Although this approach suffers from an inability to test
differences between the two homogeneous dynamics conditions, it holds .
down the total number of tests conducted in the statistical analysis.
By resulting in fewer tests, this approach alleviates some of the
concern with an escalating experiment-wise type 1 error rate. To
the extent that the experiment-wise error rate could therefore be -
ignored and type 1 error probabilities left uncorrected, the result
Is that those tests that were conducted are more powerful. Although a
differences between the two homogeneous control order conditions may
P%
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53 p
be important, they were not the focus of this study. Thus, the loss
of the ability to make such comparisons statistically was considered
worth the potential gain in power for those comparisons that were of
greatest interest.
Second, it was decided to average measures (again, except for
the strategy measures) across the vertical and horizontal axes in the
two homogeneous control order conditions. While differences between
the two axes would be important in experiments concerned with axis
independence in general, they were not of interest in the present
experiment. Similarly, control hand was not analyzed since this
variable was not of interest in this study, and its inclusion would
have detracted from the power of the rest of the analysis.
As a result, all variables--except the strategy measures--were
analyzed in two 2 X 2 X 2 (display integrality by control integrality %
by dynamic heterogeneity) analyses of variance (ANOVA), one for each £
control order. The strategy variables were analyzed in a 2 X 2 X 3
ANOVA since analysis of the control orders separately would have
defeated the purpose of the analysis.
Since the global analyses of the various dependent variables
were planned in advance of the experiment, no attempt was made to p.
gaurd against an escalating experiment-wise type 1 error rate.
Further, all of the contrasts reported within a given variable were
planned and orthogonal; thus, no attempt was made to control
family-wise type 1 error rates (see chapter 8 in Keppel (1982) for a
%'
54
discussion of this approach). There was one exception to this last
statement (in the strategy bias data, which were exploratory); in
that case, Tukey's method for correcting the family-wise error rate
was used.
Single Axis Task Baselines and Dual Axis Decrements
Ideally, single axis task performance should not have been
affected by the experimental manipulations and therefore should have
remained constant across groups. Thus, it should provide a baseline
against which to compare the effects of the experimental conditions
on all of the dual axis measures except the strategy and
cross-coherence measures. Consequently, instead of analyzing the %
dual axis measures directly, one could profitably analyze the
difference between those measures and their single axis counterparts.
Such differences will be referred to as dual axis decrements. These
decrvments were calculated individually for each subject by
subtracting that subject's single axis measure on a particular
dependent variable from his or her dual axis measure.
Two theoretically important issues are associated with dual axis
decrements, as with dual task decrements in general. First, although
decrements are empirically meaningful in and of themselves,
theoretical inferences drawn from these decrements depend upon
vertical axis tracking (for example) being fundamentally the same
under dual axis conditions as under single axis conditions. To the
extent that such equivalence is violated, decrements may be difficult
".%
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55
to interpret. A second difficulty with decrements is that their
variance is comprised of two components: one component is unique to
the dual axis task and one is unique to the single axis task. The
component of variance common to dual and single axis tracking is
removed when the decrement is computed. While the act of computing iidecrements implies that one wishes to analyze the variance component
unique to the dual axis task, it is not clear that one also wishes to
analyze the component unique to the single axis tasks.
In response to the equivalence issue, task equivalence under
single and dual axis conditions is usually assumed. The reason for
such assumption is that equivalence is virtually impossible to prove
yet is often needed in order to make any sort of theoretical
inferences possible. The second difficulty is often dealt with by
subtracting the sample single axis mean from each subjects' dual axis
score. This procedure avoids the problem of adding a single axis
variance component to the decrement variance because the sample mean
is a constant within the sample. But for the same reason,
subtracting the sample mean leaves the dual axis data essentially
unchanged except that the dual axis grand mean is lowered. Thus,
subtracting the sample single axis mean is equivalent to doing
nothing to the dual axis data. Consequently, subtracting each
subject's single axis score from his or her dual axis score seems to
be the most useful way of deriving dual axis decrements in spite of
the difficulty with respect to the unique single axis variance
.|
56
component.
Before computing dual axis decrements, an effort was made to
determine whether single axis performance was insensitive to the dual
axis experimental manipulations. While the assumption of single axis
insensitivity to the experimental manipulations held up for most of
the measures, it failed for both of the gain measures, intercept and
slope (see Damos & Lintern, 1981, for a similar sensitivity of single
axis gain). Both variables were influenced by the heterogeneity of
dynamics manipulation (p < .05) in the same direction as in the dual
axis tasks.
Because the sensitivity of single axis gain to the heterogeneity
of dynamics manipulation is most readily interpreted as a carry over
effect from the dual axis task (cf., Damos & Lintern, 1981), it
seemed prudent not to rely on dual axis decrements in the gain
measures. Consequently, both dual axis gain intercept and gain slope
were analyzed directly in place of the decrements. Decrements were
analyzed for all other variables where they were defined.
Error and Control Velocity Dual Axis Decrements
Most psychological studies of tracking behavior use error as the
dependent variable; thus, the dual axis error decrements provide the
major link between the present and previous studies. As is typically
found, all error decrements were positive, indicating that dual axis
error was greater than single axis error.
Evaluation of trials effect. Before presenting the dual axis
P [
"56 %
error decrements, it is important to evaluate the potential loss of
information about the effect of practice since the decrement measures Ile
necessarily collapse data across trials. Figures 3 and 4 display the
mean dual axis errors by trial (session 3 only) for the first and .
second order axes, respectively. Each figure displays the practice
effect for the heterogeneous and homogeneous dynamics conditions
separately.
To determine whether the practice effect varied systematically
with the eight experimental conditions, an analysis was carried out
on the linear, quadratic, and cubic components of the trials effect.
The statistical approach taken was to perform a complete 2 X 2 X 2 4. -
ANOVA on each of the three components and then to adjust the %
resulting p-values by a Bonferonni correction. This approach avoids
the difficulties of the univariate mixed model approach to
within-subjects measures and passes over the multivariate step in the
MANOVA approach to such measures (cf., Harris, 1965; O'Brien & *1-
Kaiser, 1985). (Higher order contrasts were not analyzed due to their *
uninterpretability.)
The above analysis of the errcr data by trials detected only one
marginally reliable effect of the experimental manipulations: the
quadratic component of the homogenous first order axis was larger
than that of the heterogeneous first order axis as is evident in
Figure 3, F(1,56) = 5.87, MS. = 13965.13, Bonferonni p .0549.
Since no other reliable effects were detected in either the first or
01
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58
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1 2 3 4 5 6 7 8
TRIALS
Figure 3. First order rms error over dual axis trials in session 3.This figure and the next show the effect of practice as afunction of whether dynamics on the two axes were the sameor different.
.4
NOTE: In these and the following figures, the numbers shownin parenthesis in the form (a,b) refer to control dynamics: "a refers to the dynamics on the axis represented in the .
figure, b refers to the dynamics on the paired axis (notrepresented in the figure). In all cases, data are averagedacross vertical and horizontal axes.
'
59
$=SAM DYNAMICS (2,2)+=DIFFERENT DYNAMICS (2,1)
5W0
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Figure 4. Second order rms error over dual axis trials in session 3.Again, the effect of practice is shown as a function ofwhether dynamics on the two axes were the same or different.
'C
60
second order axes, it is concluded that collapsing the error data
across trials entailed only a minimal loss of information with regard
to the experimental manipulations.
Error decrements. Figures 5 and 6 display the dual axis
decrements in root mean square error in each of the eight
experimental conditions for first and second order tracking,
respectively. In Figure 5, an effect of heterogeneity of dynamics is
evident in which the first order tracking error decrement is less
when both axes are first-order than when one Is second order, F(1,56)
- 9.48, MS. = 306.11, p = .0032. An heterogeneity effect is also
evident in Figure 6, but here the error decrement is less in the
heterogeneous condition--that is, second order tracking is disrupted
more by having second rather than first order dynamics on the other
axis, F(1,56) = 19.02, MS. = 3136.52, p < . 0001.
An interaction of display type (integrated or separated) with
heterogeneity of dynamics also appears in both figures: F(I,56)
7.14, MS. = 306.11, p = .0099 (first order axis); F(1,56) 5.91,
MS. 3136.52, p .0183, (second order axis). In both figures, the
error decrement was increased by separated displays when the dynamics
were the same on both axes (first order F(1,56) = 5.72, p < .05;
second order F(I,56) = 14.60, p < .001) but not when the dynamics
were different (first order F(1,56) = 1.91, p > .10; second order
F(1,56) = 0.15, p > .25). Although a display type by control type
interaction also seems evident in Figure 6, it was not reliable,
N N
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DISPLAY DISPLAY
How9geneous Dynamics (,) Heterogeneous flnmics (t,2)ii)
Figure 5. First order dual axis error decrement as a function of theeight experimental conditions. All dual axis decrementsreported in this study were calculated individually for eachsubject. In the present case, each subject's single axiserror was subtracted from his or her dual axis error.
::.
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62
--integrated control
i:separated control
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Figure 6. Second order dual axis error decrement as a function of the..
eight experimental conditios. , "
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63
F(1,56) = 2.65, MS, = 3136.52, p = .1089.
Control velocity decrements. While error decrements index the
deterioration of subjects' performance in the dual axis task, control
stick velocity decrements index both the change in the frequency and
average size of control stick movements. As such, they indicate
whether subjects have grown more or less cautious in attempting to
control error, assuming that control effort is unchanged. Positive
decrements (i.e., increments) indicate a decrease in caution while
negative decrements indicate an increase in caution relative to the
single axis task.
Figures 7 and 8 plot the control velocity decrements in each of
the eight conditions for the first and second order axes,
respectively. The figures are arranged so that small decrements are
plotted above large decrements.
Note that in first order tracking (Figure 7), the velocity
decrements tend to be near zero under homogenous control orders and
negative under heterogeneous control orders. For second order
tracking (Figure 8), the opposite pattern appears: the decrements
tend to be negative under homogeneous dynamics and positive under
heterogeneous dynamics. In both cases, the effect of heterogeneity
of dynamics was reliable: F(1,56) = 10.75, MS, = 4442.71, p = .0018
(first order); F(1,56) = 8.98, MS. = 21616.73, p = .0041 (second
order). Thus, the effect of heterogeneous dynamics seems to be to
increase the control velocity of the second order axis and toCl
.5
S. ~ I -. * S .
64
decrease that of the other axis. Phrased in other terms, having
second order dynamics on one axis leads to a reduction in control
velocity on the other axis.
Also evident in both figures is a display type by control type
interaction. This interaction appears to be a compatibility of
integrality effect since the control velocity decrement is less when
controls and displays are both integrated or both separated than when
one was integrated and the other was integrated. This interaction
was reliable in the first order task (F(1,56) = 5.02, MS., = 4442.71,
p = .0290) but not in the second order task (F(1,56) = 1.63, NS. =
21616.73, p = .2070).
Closer examination of the interaction revealed that when
controls were integrated, display integrality had no reliable effect
on control velocity, F(1,56) 1.25, p > .25; but when controls were
separated, then separated rather than !ntegrated displays led to
smaller decrements in control velocity, F(1,56) = 4.20, p < .05.
Control Theory: Human Open Loop Transfer Functions
According to the Cross-Over model of human tracking performance,
the human will adjust his or her own open loop transfer function so
that the human-control system open loop transfer function is first
order. Thus, if the control system is already first order, the human
will act like a zero order system with a gain slope of zero dB per
decade and a phase intercept of zero degrees. That is, a perceived
error position will generate a proportional controlled response
S. "
O integrated controlde=separated control
,-.5
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integrated separated integrated separated
DISPLAY DISPLAY
Homogeneous Dqnamics (i,1) Heterogeneous Dqnamics (1,2)
Figure 7. First order dual axis control velocity decrement as a
function of the eight experimental conditions. In this and
the next figure, points plotted higher in the figure
represent smaller decrements.
5%~~~- .' ..
66
0 integrated control
= separated control
0
0 iu 5
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integrated separated integrated separated
DISPLAY DISPLAY
Homogeneous Dynamics (2,2) Heterogeneous Dynamics (2,1)
Figure 8. Second order dual axis control velocity decrement as afunction of the eight experimental conditions.
VI
67
position. But if the control system is second order, then the human
will act like a minus-first order "lead generating" system with a
positive gain slope of 20 dB per decade and a phase intercept of 90
degrees. That is, a perceived error velocity will generate a
proportional controlled response position.
Figures 9 and 10 display the average transfer function Bode
plots for single and dual axis tasks. (Single axis phase functions
were indistinguishable from the dual axis functions and so are not
shown.) Table I displays the gain intercept, gain slope, phase
intercept, and effective time delays for the axes shown in both
figures. Figure 9 is for the first order axes and Figure 10 is for
the second order axes. N.te that the first order gain slopes are all
slightly positive (about 6 dB per decade) while the phase intercepts
are around -2 degrees. The second order gain slopes are much steeper
(about 14 dB per decade) with phase intercepts around 28 degrees.
These data indicate that subjects did respond to the first order task
by adopting an essentially zero order open loop response. While
subjects' response to the second order task was not optimal with
respect to the cross-over model (a gain slope of 20 dB per decade
with a phase intercept of 90 degrees), it was essentially a minus
first order response to a second order system.
The phase plot of both figures shows a lag increasing
exponentially at higher values of log frequency. This lag represents
the contribution of a constant effective time delay. The effective
1b:
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* =dual axis, homogeneous dynamics (1,1)
0- dual axis, heterogeneous dnanios (,2) ,
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Figure 9. First order axis subject open loop responses for the singleand dual axis tracking tasks under homogeneous andheterogeneous control dynamics. Plotted gain and phasepoints are the observed data averaged across subjects.Least squares estimates of the gain and phase functions arealso shown. Single and dual axis phase data areindistinguishable in this figure.
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....... .... .. .Figure,. ... 10 eon rerai subject open. loop.. responses for, the , .,-.. ,.,/_.
.1
70
Table 1
Dual and Single Axis Human Open Loop Transfer Functions: Gain and
Phase Data
Gain Gain Phase Effective
Intercept Slope Intercept Time Delay
(dB) (dB/dec) (degrees) (ms)
First Order Axis
Single axis -1.13 5.65 -1.970 232
Dual axis
Same Dynam -3.56 5.52 -3.30 245
Diff Dynam -8.65 7.78 0.80 242
Average -4.45 6.32 -2.02 240
Second Order Axis
Single axis -1.03 15.49 35.53 344
Dual axis 'A
Same Dynam -5.85 12.96 23.09 319
Diff Dynam -3.00 13.04 23.97 340
Average -3.29 13.83 27.53 334
VS
time delay measures (i.e., phase slope; see "Data Analyzed" for the
linearizing transformations used) conform well to those specified by
McRuer and Jex (1967) in their review of human open loop transfer
functions. When applied to the bandwidths used in the present study
of 2.4 and 3.1 radians per sec, their review suggested a first order
effective time delay of 175 to 200 ms and a second order time delay
of about 320 to 350 ms. The corresponding effective time delays
obtained here were about 240 and 334 ms, respectively.
Gain. Figures 11 and 12 display the gain intercepts for first
and second order axes in each of the eight experimental conditions.
Figures 13 and 14 similarly display the gain slopes. Only the Z.
heterogeneity of control dynamics reliably influenced the gain
intercepts for either task (Figures 11 and 12). For the first order
axis, the gain intercepts were attenuated when the control dynamics
were second rather than first order on the other axis, F(1,56)
6.98, MS. = 59.52, p = .0107. For the second order axis, the gain
intercepts were likewise attenuated when the control dynamics were
second rather than first order on the other axis, F(1,56) = 4.47,
MS- = 29.18, p = .0390.
Notice that the effect of dynamics heterogeneity on gain is the
same as its effect on control velocity reported above. This
correspondence is expected since both measures express, in different
domains, the amount of control activity expended to reduce perceived
error. In both cases, control activity is diminished when second
~'a 'a,.
72
-integrated control
9 separated control ",
I ...
I4 -6e
CCI , '
N - Sj ... 0"E
/.-.
integrated separated integrated separated
DISPLAY DISPLAY
Homogeneous Dgnamics (1,i) Heterogeneous DynaMics (1,2)
Figure 11. First order dual axis gain intercept of subjects' openloop responses in the eight experimental conditions. Gainis measured in decibels.
'a
;., . % % .7". '% %, . "-.",. , , • . . .-. % % % .. % . ".' . % . , . ' , % .. •. 0-
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73
O " integrated oontrol
separated control "I
-3'
6
ERCE -T
%%
I -',.,
-13 %
integrated separated i ntegrated separated
DISPLAY DISPLAY
Homogeneous ynamics (2,2) Heterogeneous Dynamics (2,1)
Figure 12. Second order dual axis gain intercept of subjects' open %loop responses in the eight experimental conditions, Gainis measured in decibels.
FAR' J YF: : : E TFW,: ; I - ,V ,,,' ,?%I, -J k l ww -Kv . . ..
74
= integrated control
- separated control
15
S i8
I A
L
0V
integrated separated integrated separated
DISPLAY DISPLAY
Hoogeneous Dynamics (,) Heterogeneous ynalcs (1,2)
Figure 13. First order dual axis gain slope of subjects' open loopresponses in the eight experimental conditions. Slope isexpressed in decibels per decade.
A5
75 N
Q integrated control
s eparated control
151
A O
0PE
54P
integrated separated integrated separated
DISPLAY DISPLAY
Homogeneous 09namics (2,2) Heterogeneous 09namics (2,1)
Figure 14. Second order dual axis gain slope of subjects' open loopresponses in the eight experimental conditions. Slope isexpressed in decibels per decade.
:% % %
76
order dynamics are present on the other axis, an effect well
replicated in the literature (Wickens, 1986b; Gopher & Wickens,
1977).
Dynamics heterogeneity affected gain slopes in the first order
axis (F(1,56) = 4.11, MS, = 19.85, p = .0474) but not in the second
order axis (F(1,56) = 0,01, MS. = 20.49, p > .93). That is, the
presence of second order dynamics on one axis steepened the first
order gain slope, but the presence of first order dynamics on one
axis had no effect on the second order gain slope.
Although dynamics heterogeneity had no affect on second order
gain slope, control type did. Second order gain slope was steeper
when an integrated control was used for both axes rather than when
separate controls were used, F(1,56) 8.94, MS. 20.49, p .0041.
The same effect was absent in the first order gain slope (p > .96).
Phase. Phase intercept was not reliably influenced by any of
the dual axis experimental manipulations. The overall first and
second order dual axis decrements in phase intercept were reliable,
however. The first order phase intercept declined 7 degrees in dual
axis tracking, F(1,63) = 9.24, MS. = 0.002 (units in radians),
p = .0035; the second order intercept declined by 12 degrees,
F(1,63) = .04, MS = 0.002 (units in radians), p < .0001.
As reported above, the presence of second order dynamics on one
axis steepened the first order gain slope. One interpretation of
this effect is that the second order axis may have induced subjects
...
to needlessly generate a small amount of phase lead in the first
order axis. If so, then one would expect the first order phase
intercept of subjects tracking with heterogeneous dynamics to be
higher than that of subjects tracking with homogeneous dynamics. The
first order phase intercept of the heterogeneous dynamics group was
in fact 4 degrees higher than those in the homogeneous dynamics
group, but the effect was not statistically reliable, F(1,56) = 1.37,
MS. 0.06 (units in radians), p = .2460.
Unlike phase intercept, effective time delay (phase slope,
computed as described earlier) was influenced by the dual axis
experimental manipulations under second order tracking. (No reliable
effects were observed under first order tracking; MS. = 0.009, units
in seconds.) Figure 15 displays the dual axis decrement (i.e., the
increase) in effective time delay in the second order axis for each
of the eight experimental conditions. The figure is arranged so that
small decrements are plotted above large decrements.
These decrements in effective time delay show the display type
by control type interaction expected if a mapping operation is
required when the integrality of displays and controls do not match.
That is, effective time delay was 132 ms shorter when display and
control type were both the same (i.e., integrated or separated) than
when one was integrated and the other was separated, F(1,56) = 6.46,
MS. = 0.011 (units in seconds), p = .0138. Examination of this
interaction showed that control integrality had no reliable effect
0'
78
0= .ntegrated control
= separated control
EFFECI "
.0 3 5 " /E
T
HE
.808 a
D -,a35E C0REM
T integrated separated integrated separated
DISPLAY DISPLAY
Hoogneu DyiHk (2,2 H'1I% I. etreeous DynaioCs Q" (2)
Figure 15. Effective time delay decrement in the second order axis foreach of the eight experimental conditions (in seconds). Ncsignificant effects appeared in the first order axis.Points plotted higher in the figure represent smallerdecrements.
!mmm~m m mll~m N
79
when displays were integrated, F(1,56) = 1.77, p > .10; but when
displays were separated, separated controls led to shorter time
delays than did integrated controls, F(1,56) = 5.14, p ( .05.
Cross-Coherence. Primary cross-coherence (coherence between the
input signal to one axis and control stick movements in the other
axis) is shown in Figures 16 and 17 for the first and second order
control axes, respectively. Both figures suggest that primary
cross-coherence was greater with integrated rather than separated
controls and possibly with integrated rather than separated displays.
The control type effect was reliable in both the first and second
order axes, F(1,56) = 4.73, MS, = 0.007, p = .0338, F(1,56) = 8.20,
MS., = 0.004, p = .0059, respectively; the display effect, however,
was not strongly reli. e for either control order (p = .0820, p =
.1106, respectively). No other effects were statistically reliable
in either figure, including the main effect of heterogeneity. That
is, the increase in RMS error decrements in the first order axis with
second order dynamics on the other axis does not seem attributable to
cross-coherence.
Secondary cross-coherence, defined only in the separated-S.
controls condition, may be thought of as an index of confusions
between control sticks. This type of cross-coherence is displayed in
Figure 18 for the first and second order axes. It is evident that
secondary cross-coherence was greater given an integrated error
display rather than two separate error displays, F(1,28) 11.38,
'p
=integrated control I
A p
= separated control
PR
IA *
R V-R
S .2
0HER .1ENC
integpated separated integrated separated
DISPLAY -DISPLAY
Homogeneous Dynaxics (1,1) Heterogeneous Dynamics (1,2)
Figure 16. First order primary cross-coherence (i.e., confusionsbetween which signal goes to which axis) in the eightexperimental conditions. Cross-coherence is the controltheory equivalent of a squared correlation and may beinterpreted as such.
N '
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, separated control
P
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integrated separated integrated separated
DISPLAY DISPLAY
Homogeneous Dynamics (2,2) Heterogeneous Dynamics (2,i)
Figure 17. Second order primary cross-coherence in the eightexperimental conditions.
."S
I
82
0 homogeneous dynamics
heterogeneous dynamics
~(2,i)E (iii) I&
0"A (22)
C
.2
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integrated separated integrated separated%
DISPLAY DISPLAY
FIRST OR0ER HXIS SECONO OROER HXIS
8 .24
Figure 18. Secondary cross-coherence (i~e., confusions betweenwhich stick controls which axis) in each applicablecondition. Secondary cross-coherence is defined only whenseparate control sticks are used for the two axes Notethat confusions between control sticks do not directly
affect the error in either axis.
- 7I
83
MS-, = 0.0135, p = .022 F'1,28) = 13.73, MS-. = 0.021, p = .0009,
respectively. No effects of dynamics heterogeneity are apparent in
the figure and none were detected statistically.
Alternating versus Simultaneous Control Strategies
The strategy measures (i.e., the length and angle of the
strategy vector as described earlier) are shown in Figures 19 and 20.
Recall that the switching measure may be thought of as the distance
of the subject's response strategy away from pure parallel control.
(This distance measure is less than, but monotonically related to,
the proportion of time subjects spent alternating between axes rather
than controlling both simultaneously.) In Figure 19, the response
strategy of subjects in the homogeneous control order conditions
appears to have been closer to a parallel strategy than that of
subjects in the heterogeneous dynamics conditions. Note, however,
that all three groups of subjects spent the majority of their time
controlling in both axes simultaneously.
The main effect for the heterogeneity manipulation was reliable,
F(2,84) = 2.98, MS., = 0.009, p = .0564; and Tukey's test for pairwise
comparisons showed that while both first and second order homogeneous
subjects differed from heterogeneous subjects (p < .10), the
homogeneous subjects did not differ from each other. No other
reliable effects were found among the switching measures.
As explained earlier, the bias parameter measures the deflection
of the strategy vector in degrees from an unbiased 45 degrees. Thus,
%%
84
an unbiased strategy vector would have a deflection of zero degrees,
and the maximum deflection possible is plus or minus 45 degrees. As
with the switching measures, the heterogeneity effect was reliable,
F(2,84) = 46.29, MS., = 211.89, p < .0001. Subjects in both the first
and second order homogeneous dynamics groups were relatively unbiased
(positive 3.10 and 3.67 degrees deflections, respectively) while
subjects in the heterogeneous dynamics groups were strongly biased
toward the second order axis (a positive 33.71 degrees deflection).
Although a possible display by control interaction may exist
among the bias measures (especially in the homogeneous groups), it
was not reliable (F(1,84) = 3.04, MS., = 211.89, p = .0848). The main
effect for control integrality was statistically significant,
however; F(1,84) = 4.88, MS., = 211.89, p = .0299. The nature of this
effect is that subjects were more likely to be biased toward the
vertical axis. But recall that, for purposes of the statistical
analysis, the second order axis in the heterogeneous dynamics groups
was arbitrarily re-labeled as the "vertical" axis (in reality, the
second order axis was the vertical axis for only half of the
subjects). Thus, this main effect means that heterogeneous dynamics
subjects were more likely to be biased toward the second order axis
if controls were separated rather than integrated.
Apparently, subjects spent the majority of their time
controlling both axes simultaneously. But the data suggest that
heterogeneous subjects frequently stopped controlling the first order
N 1
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85vN.
I''N
0 = integrated control
* = separated control
oo 20-- -- 0 "a
T
C tE
F I
P ,a.Ai
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int sep int sep int Sep
DISPLAY DISPLAY DISPLAY
Dynaxics: Ll Dgnamios: 2,2 DynaMics
Figure 19. Distance of subjects' response strategies from simultaneouscontrol in each of the 12 experimental conditions. These -
Euclidian distance measures are less than but monotonicallytt.
related to the percent of time subjects spent alternatingcontrol between the vertical and horizontal axes. Ir
-'a
0
-a' 4-~' V - ~ :-~>-c-;- -.- .. y.7..\.7ycg -'v- *- 44 -~. No
86
o integrated control
= separated control
i-0
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I 2i".E ~6RE N 4'
EN
int sep int sep int sep
DISPLAY DISPLAY DISPLAY
Dynawics: 1,1 Dnaics 2,2 Dnaics: 1,2 / 2,1
Figure 20. Biases of subjects' control strategies toward one axis orthe other. The bias measure can range from -45 to +45degrees. In the two left-most panels, a positive biasmeans that subjects controlled in the vertical axis morethan in the horizontal axis. In the far right-hand panel,a positive bias means that subjects controlled in thesecond order axis more than in the first order axis.
0,
87
axis in order to control the second order axis alone. In contrast,
when homogeneous subjects adopted serial control, they divided their
time equally between the vertical and horizontal axes.
Summary of Results
The present study was designed to evaluate the impact of display
integrality, control integrality, and heterogeneity of control
dynamics on dual axis tracking performance. All three variables
influenced performance. Following is a summary of the major
findings.
First, there was a major effect of the order on a paired axis:
second order tracking consistently increased the error on the axis
with which it was paired. This effect appears to be an effect of the
demand of second order tracking, not of the heterogeneity of
dynamics.
Second, in keeping with the demand effect, subjects decreased
their control velocity and control gain when the dynamics on the
other axis were second rather than first order. This effect was
observed in both first and second order control. In addition, the
response strategy measures showed that bomogeneous control subjects
were not biased to control either axis over the other, while '
heterogeneous control subjects were strongly biased to control the
second order axis over the less demanding first order axis.
Third, overlaid on this effect of dynamics was an interaction
with display integrality. When tracking dynamics were homogeneous.
i%
V_ V- -Jfv -V7- 3-1 TV X- XT I-F7N: t V n,
88
integrated displays led to less tracking error than did separated
displays; but ihen dynamics were heterogeneous, display integrality
had no effect. This particular interaction was not evident in any of
the other response measures.
Fourth, although not evident in the error data, a compatibility
of integrality effect appeared in both control velocity and effective
time delay decrements. Statistical analysis of this effect showed
that the effect manifested itself differently in the two control
orders. When there were mismatches between the integrality of
displays and controls, subject's second order effective time delay '
increased and their first order control velocity decreased, both 'a
symptoms of less effective tracking performance.
Fifth, when first order tracking was shared with second order
tracking, the presence of the second order axis steepened the gain
slope and but did not reliably raise the phase intercept of the
subjects' first order response. Thus, the presence of second order
dynamics on one axis influenced subjects' response to the first order
axis, but it is not clear whether that influence modified the order
of subjects' response. 2'
Finally, integrated controls led to greater primary
cross-coherence (confusions between axes) than did separated
controls, and integrated displays led to greater secondary 'a
cross-coherence (confusions between control sticks) than did
sepa:-ated displays.
VS.'p
DISCUSSION
The present study had two goals. One was to examine how the
integrality of displays and controls interact with each other and
with the heterogeneity of control dynamics to shape dual axis
tracking performance. The other goal was to place this interaction
into some theoretical context that would facilitate generalization to
manual control tasks such as exist in aviation. Three theoretical
approaches were considered as potential components of whatever
framework might finally emerge: resource theory, confusions theory,
and Wickens' (1986c) compatibility of proximity hypothesis.
The outcome of the present experiment with respect to these two
goals is summarized in Figure 21. This figure represents a
theoretical framework incorporating resources, confusions, and the '
compatibility rf proximity. Arrows indicate main or interaction
eflects of the three manipulations in the center on the inferred
processing mechanisms in the columns. As the figure suggests,
resource and confusions theory together account for the costs
associated with the various experimental manipulations while
compatibility of proximity describes the benefits.
Contrary to the claims of Navon (1985; Navon & Miller, 1986),
the data show a dissociation of confusions from demand effects which
suggests that the two are quite different things. On one hand,
confusions (that is, primary and secondary cross-coherence) were
greater when controls or displays were integrated rather than
" 9
90
separated. But on the other, tracking error increased with
separated--not integrated--displays, and the bandwidth of stable
second order tracking (related to gain slope) decreased with
seperated, not integrated, controls.
Further, although confusions are apparent in the primary and
secondary cross-coherence measures, resource demand and the
compatibility of proximity seem to account for the major experimental
effects. First, in keeping with resource theory, heterogeneity of
control dynamics per se had no effect on performance; rather,
tracking under both first and second order dynamics benefited if the
dynamics on the other axis were first order and suffered if they were
second order. Second, consistent with the compatibility of proximity
hypothesis, dual axis tracking suffered given separated displays if
the control dynamics on the two axes were the same but not if they
were different. Third, a compatibility of integrality effect
appeared in which performance benefitted when the integrality of
displays and controls matched but suffered when they did not match.
These effects were not generally accompanied by changes in
confusions. Nevertheless, beyond these three effects, confusions
were evident when integrated rather than separated displays and
controls were used. These findings will now be discussed in turn.
Heterogeneity of Control Dynamics
Evidently, the improvement in second order tracking error under
heterogeneous dynamics is attributable to the fact that first order
.5.
.5-
-9I
oEEcFlIS NiPULMTION OsoriSCoHpalibilii yCnfsosRe~re
RMS Error
DYNAMICS Gain Slope 0) Gain Intercept(first order
Proximity axis) Control Uelocity
Co patibilit.(scanningstrategy)
Secondary kMS ErrorDISPLAY Coherence (visual
(irrelevantscanning"
Transformation ontrol ,tion)Compatibeility(effective
controlay Primary Gain Slope
velocity) CONTROL Coherence (bandwidth of(incorrect stable control.movement second order
directiiri axis)
P:;':r~. A mclPK It r 3 .:cn c: nTj~rs, resource- rmpe.iti n. 3n.: ; g'!!~ c *he experimental ,
man:-, i Jn7 :t *-e resent ='ud;v. See the text forir er -yX j"l n .
0i:
65 71 RESOURCES CONFUSIONS ND COMPATIDILITY IN bURL AXIS 2/2TRACKING: DISPUWS CO. (U) AIR FORCM INST OF TECH
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92
dynamics are simply less demanding than second order dynamics. Thus,
when first rather than second order dynamics are on one axis, there
are more resources available for tracking on the other axis. The
greater availability of resources then always led to a reduction in
tracking error. This single principle then easily accounts for the
increase in first order error and the decrease in second order error
under heterogeneous compared to homogeneous control dynamics.
As was indicated in the introduction, people may become more
cautious or may reduce their control effort when their processing
resources are overtaxed. In a tracking task, this increased
conservatism may then lead people to attenuate their control
activity, as evidenced in control gain and control velocity (Wickens,
1976; Wickens & Gopher, 1977). In the present experiment, whenever
the dynamics on one axis were second order, subjects attenuated their
control gain and velocity on the other axis. But when first order
dynamics were on one axis, the attenuation of gain and velocity on
the other axis was considerably less. These results are consonant
with other studies likewise showing gain attenuation under increased
resource demand (e.g., Baty, 1971; Damos & Wickens, 1980; Damos &
Lintern, 1982; Levison, Elkind, & Ward, 1971; Wickens, 1976; Wicker'-
& Gopher, 1977). If control order confusions had been predominant,
this is not the pattern that should have been observed. Rather, gain
and control velocity should have always been attenuated under
heterogeneous dynamics to a greater extent than under homogeneous
I
I.F .r .' -. .' e .* F '% % .
% % '° -%'" .% "2 ," '- • -%J' ' " ' "-"'-'"; " " . "--- " "o ,' X. -- - -. - ..P- --P
UNAp
93
dynamics.
Further evidence for a demand interpretation of the
heterogeneity data appears in the results of the response strategy
analysis. That analysis showed that while homogeneous subjects
tended to control both axes to the same degree, heterogeneous
subjects were more likely to concentrate primarily on the second
order axis. In addition, many of the 32 subjects in the
heterogeneous dynamics groups commented that they had tried to
concentrate on the secc.d order axis while occasionally checking to
ensure that first order error was "acceptable" (more is said about
this strategy in the next section). Thus, it appears that the
greater difficulty of minimizing second order error led heterogeneous
control subjects to allocate most of their attention to the second
order axis.
This attention allocation strategy may explain the increase in
first order gain slope under heterogeneous control dynamics. The
increase in slope would have resulted if heterogeneous subjects
selectively attenuated the gain of their response to the lower input
frequencies while responding mainly to the higher, more salient input
frequencies. If they were attending mainly to the second order axis
and only occasionally controlling the first order axis, then the
outcome of responding mainly to the higher first order frequencies
would seem to be likely. In addition, this attentional strategy
would also account for the absence of a corresponding increase in the
N -. -
94
subjects' phase intercept (that should have resulted if control order
confusions were present), and for the absence of any effect in the
second order axis. Thus, even the steeper first order gain slope
under heterogeneous dynamics may provide evidence for a demand
interpretation of the heterogeneity data rather than for control
order confusions (although the latter interpretation can not be ruled
out with certainty).
Display Integrality and the Heterogeneity of Dynamics
Wickens' (1986c) compatibility of proximity hypothesis predicts
the interaction between display integrality and dynamics
heterogeneity apparent in Figures 5 and 6. According to Wickens'
hypothesis, tracking under heterogeneous dynamics should benefit from
separated rather than integrated displays. In the present context,
this benefit could have arisen either because separated displays
helped subjects to.avoid control order confusions (cf., Chernikoff &
Lemay, 1963) or because the biased control strategy associated with ,
heterogeneous dynamics was easier to carry out with separated
displays. The main difficulty with the hypothesis that separated
displays attenuated control order confusions is that there is no
reliable evidence for a display effect in the gain slope data (see
Figures 13 and 14) where such an effect would have to be found.
Evidence concerning whether separated displays may have facilitated a
biased control strategy is presented next.
To see how the biased control strategy of subjects in the
ev,-.
% %.
_|
95
heterogeneous dynamics conditions (depicted in Figure 20) may account
for the above interaction, first consider those subjects in the
homogeneous dynamics conditions. If it is assumed that control
strategy biases are directly related to attentional biases, then it
can be said that these subjects were unbiased and so allocated
attention equally between the two axes. Thus, they attended equally
to both vertical and horizontal errors even when displays were
separated. Because separated error displays required some degree of
visual scanning, the increase in tracking error associated with such
scanning is evident for these subjects in the left panels of Figures '0
5 and 6 (cf., Allen, Clement, & Jex, 1970; Baty, 1971; Levison &
Elkind, 1967; Levison, Elkind, & Ward, 1971).
Now consider subjects in the heterogeneous dynamics conditions.
As seen in the strategy bias data, these subjects do not appear to
have attended equally to both errors (again, assuming that response
bias is directly related to attentional bias). In unsystematic
self-reports, many of these subjects claimed to have used the
following strategy. First, these subjects began a trial by reducing
the first order error to some subjectively acceptable level. Because
the disturbance signal was a sum of sinusoids, first order error
would then remain "acceptable" in the absence of further control
activity. Examination of the time series data for these subjects
showed that they accomplished this goal in the first 2 or 3 seconds
of the trial. Then, according to their self-report, these subjects
96
focused their attention on the second order cursor for the remainder
of the 120 second trial while occassionally checking the magnitude of
first order error via peripheral vision. If first order error seemed
to be growing "too large", then these subjects would initiate
corrective control actions while continuing to focus mainly on the
second order error.
One difficulty with the interpretation based upon these self
reports is that the strategy data displayed in Figure 19 indicate
that heterogeneous subjects may have controlled in both axes
simultaneously at least 80 percent of the time. This apparent
contradiction may have arisen from the conservative criterion used to
decide when subjects were not controlling in an axis (i.e., no
deflection of the appropriate control stick). For many subjects,
this conservative criterion may have underestimated the time they
actually spent controlling just one axis at a time, and overestimated
the time controlling both axes in parallel.
If heterogeneous subjects given separated displays adopted the
foregoing attentional strategy, then they clearly engaged in little
if any visual scanning. Thus, the scanning cost present under
homogeneous dynamics would be absent under heterogeneous dynamics.
This is precisely the effect seen in Figures 5 and 6. But the
compatibility of proximity hypothesis also requires that integrated
displays inhibit the biased control strategy. From Figure 20, it is
clear that display integrality had no effect whatever on control
5.
• 5' % , . - % % " , - - ..- , . ., -
bias. Further, no systematic effect of display integrality on
heterogeneous tracking error is apparent in the right panels of
Figures 5 and 6. The question then is whether control bias itself is
sufficient to account for the display by dynamics heterogeneity
interaction with out reference to the compatibility of proximity
hypothesis. From the present data, the answer to this question
appears to be "yes". Yet the interaction is predicted by the
compatibility hypothesis and is in agreement with a large body of
other data also pointing to the compatibility hypothesis (see
Wickens, 1986c, for a review).
One might say, therefore, that the present data support
compatibility of proximity as an intervening variable but not as a
hypothetical construct (MacCorquadale & Meehl, 1948; Gopher, 1986).
An intervening variable is a convenient label given to a class of
experimental procedures and the set of outcomes to which they
consistently give rise. Thus, compatibility of proximity as an
intervening variable integrates the present data into the large body
of other data that is subsumed under the hypothesis. On the other
hand, a hypothetical construct refers to an internal psychological
process that in some sense is independent of the experimental
manipulations used to detect it. It is compatibility as a
hypothetical construct that seems unnecessary to account for the
present data.IL
One possible objection to the "strategy without compatibility"
%.
98
account of the display by dynamics heterogeneity interaction is that
it implies psychological equivalence of the integrated and separated
displays under heterogeneous dynamics. Equivalence, in turn, implies
that display integrality was completely irrelevant under
heterogeneous dynamics. If this were in fact the case, then there
could be no display effects of any kind with respect to any
independent variable under heterogeneous dynamics. This implication
is clearly wrong, however, because there were effects involving
display integrality that remained reliable under heterogeneous
control dynamics. These effects were evident in the control
velocity, effective time delay, and secondary cross-coherence
measures (and are discussed in the next two sections). But this
objection can be answered by noting that a biased attentional
strategy need only have attenuated the psychological difference
between displays. If this attenuation was sufficient to render
display integrality irrelevant with respect to tracking error but not
with respect to some other dependent measures, then the present set
of results are consistent with the "strategy without compatibility"
hypothesis.
Finally, interpretation of the display by dynamics heterogeneity
manipulation as a strategy effect should raise a caution that
heretofore has not been recognized. Chernikoff and Lemay (1963)
found exactly the same interaction and took it to mean that separated
displays helped subjects to avoid such confusions. Other writers
4|
99
have echoed that interpretation, suggesting that it may be a useful
principle of display design (see Wickens, 1984a, 1987a,b for
reviews). But if the strategy interpretation is correct, then
Chernikoff and Lemay's conclusions are misleading at best--and could
be dangerous under the right circumstances. While the strategy of
allocating attention primarily to just one of the two tracking axes
may be viable in the laboratory where the inputs are sinusoidal, it
could be fatal in a high-speed aircraft. This makes it seem unlikely
that pilots, for example, would actually employ such a strategy.
Consequently, the finding of no penalty to separated displays under
heterogeneous dynamics may have little generality beyond the safety
of the laboratory.
An implication of the foregoing strategy interpretation is that
integrated displays lead to less tracking error than do separated
displays as long as attention is allocated equally to both tracking
axes. Yet integrated displays also appear to lead to more confusions
between control sticks (secondary cross-coherence). This result
parallels a similar finding with respect to control integrality and
confusions between axes. How these findings may be understood is
discussed in the next section.
Control Integrality
Unlike many studies (Baty,1971; Bartram et al., 1985; Levison et
al., 1971; Regan, 1960), the present study found that tracking error
was unaffected by control integrality. Importantly, the superiority
I.1
100
of separated controls with heterogeneous dynamics reported by
Chernikoff and Lemay (1963) is completely absent. Why control
integrality had no effect on error in the present study is not known.
With respect to the Chernikoff and Lemay study, one possibility is
that the difference between the first and second order dynamics used
in the present experiment is less than that between the zero and
second order dynamics used by Chernikoff and Lemay; thus, a
compatibility of proximity effect between control integrality and
control dynamics may have been less likely in the present study.
However, this difference does not account for the discrepancy with
the other studies just cited which did not use heterogeneous control
dynamics but found a consistent cost to separated controls. One
important difference between the present experiment and those other
studies is the experimental design used. While those studies
manipulated control integrality within subjects, the present
experiment did so between subjects.
Perhaps the influence of control integrality on tracking error
in within-subjects designs is mediated by what might be called a
"contrast effect". That is, a decrease in tracking error associated
with integrated controls may not result from the fact that the
control is integrated per se, but from the subject's perception that
tracking seems easiest with the integrated rather than the separated
controls. This perception, in turn, might then lead to a
"self-fulfilling prophecy" in which subjects expect to perform more
e
.%~
poorly with separated controls and therefore do perform more poorly. .9
Whether such a contrast effect occurred in the cited experiments
is another question, but the fact that the possibility can not be
ruled out is one of the hazards of a within-subjects design (cf.,
Matthews, 1986; Poulton, 1974, 1982). If a contrast effect was-4
operating in those earlier studies, then the present data may present r
a more accurate picture of the effect of control integrality on
tracking error. Future research may be able to clarify this picture
by specifically comparing the performance of subjects who track under
both control integrality conditions with subjects who track under
just one integrality condition.
While tracking error was not influenced by control integrality,
confusions were affected. Just as display integrality led to more
control stick confusions (secondary cross-coherence) than did k
separated displays, so integrated controls led to more axis
confusions (primary cross-coherence) than did separated controls.
Confusions thus appear to be most likely when signals are transmitted
via a common channel; in this case, a common control hand. Navon and
Miller (in press) suggest the metaphor of two telephone lines that
have become crossed. In terms of this metaphor, it seems that the
probability of crossed lines is significantly diminished when the
lines travel through separate rather than common cables.
As is evident, these confusions did not lead to greater tracking
error. Nor do they appear to have had any other deleterious effects
-V
102
on subjects' tracking performance. Indeed, the optimality of
subject's second order transfer function (as indexed by gain slope, a
determinant of the bandwidth of stable control) appears to have
improved with an integrated control in spite of the attendant
confusions. This fact, coupled with the superiority of tracking with
integrated displays, suggests that confusions generally may not be
able to account for task decrements in at least some task paradigms
as Javon (1985; Navon & Miller, in press) has claimed.
This dissociation between confusions and other measures suggests
that the two reflect different underlying processes. Confusions may
represent cross-talk between signals (cf., Wickens, 1987b) while
error and open loop gain may mainly reflect competition for scarce
resources.
Control and Display Compatibility
An important interaction was found between the integrality of
displays and controls. This interaction was of the form suggested by
Baty (1971); that is, tracking benefitted when controls and displays
were both integrated or both separated, but suffered when one was
integrated and the other was separated. Significantly, this effect
was absent in the error data, appearing only in the control velocity
and effective time delay measures. This result may suggest either
that the compatibility of integrality principle is not of great
practical importance in dual axis tracking, or that it may be
important only under higher levels of demand or stress than were used
J
.~. .,j..-..s.- -- -. .' . ~ ;vc'..'-.--'~- '
i03
here.
Nevertheless, the theoretical implications of the effect seem to
be significant. First, the fact that effective time delay increased
with mismatches of display-control integrality supports the
hypothesis that subjects needed to perform some kind of cognitive
transformation of the error display under such circumstances. In the
introduction, these transformations were called "mapping operations".
Since effective time delay under incompatible display-control
configurations averaged about 130 ms longer than under compatible
configurations, this figure may be taken as an estimate of the
duration of such mapping operations (see Pachella, 1974, for the
restrictive assumptions underlying subtractive logic).
Second, the cross-coherence data gave little evidence of the
compatibility effect. Confusions between control sticks (secondary
cross-coherence) were greater with integrated rather than separated
displays as would be expected assuming occasional failures of the
mapping operations (cf., Garner, 1974; Garner & Fefoldy, 1970). But
confusions between which signals went to which axes (primary
cross-coherence) were unaffected by display integrality; rather, such
confusions were consistently greater with integrated rather than
separated controls. Thus, confusions due to mapping failures appear
to have been rare.
Third, because the compatibility effect was evident in the
display by control integrality interaction in the control velocity
- A
104
data, the underlying mapping operations may be resource consuming.
Attenuated dual axis control velocity (relative to single axis
tracking) may suggest that subjects have grown more cautious, a
response consistent with increased resource demand (Baty, 1971; Damds
& Wickens, 1980; Damos & Lintern, 1982; Levison, Elkind, & Ward,
1971; Wickens, 1976; WJckens & Gopher, 1977). If so, then one would
also expect a corresponding decrease in control gain. Since such a
decrease in gain was not found, the demand of these operations for
resources may be slight. This slight demand combined with the rarity
of confusions attributable to mapping failure may explain why the
compatibility of integrality effect was absent in the tracking error
data.
Re-evaluation of Chernikoff and Lemay (1963)
Chernikoff and Lemay's (1963) data have generally been cited as
evidence for the important role of confusions in dual axis tracking
(e.g., Levison & Elkind, 1967; Wickens, 1984a,-1987b). The present
results suggest that the significance of those early data need to be
reconsidered. As mentioned above, their finding that the scanning
cost associated with separated displays disappeared under
heterogeneous control dynamics appears to be reliable. But it also
appears to result from the strategy subjects adopt to perform the
task, not from control order confusions that are somehow alleviated
by separated displays.
As indicated earlier, another one of Chernikoff and Lemay's
%J . . L .. .a .
105
findings appears to have been less robust; namely, their finding that
tracking error under heterogeneous dynamics was greater with
integrated rather than separated controls. Although the present
control integrality interaction effect was in the "right direction"
in the first order axis, the effect was in the opposite direction in
the second order axis and was unreliable in both cases. One may
speculate that the discrepancy between experiments arose because, as
was pointed out earlier, the difference between the zero and second
order dynamics used by Chernikoff and Lemay is greater than that
between the first and second order dynamics used here. A direct
comparison between both pairs of control orders will be needed to
finally resolve this issue. In the absence of such a direct
comparison, one can not dismiss the possibility that the statistical
significance of the effect in Chernikoff and Lemay's experiment is
due to a type 1 error, some sort of contrast effect, or an improperly
balanced design. At the present time, therefore, the present data
remain inconclusive as to whether control integrality interacts with
dynamics heterogeneity in any systematic way.
If Chernikoff and Lemay's data are distorted by the unbalanced
within-subjects design which they used, then any attempt to interpret
any of their findings seriously is bound to be risky. But it is
tempting to speculate as to why they found tracking error to be
greatest under heterogeneous dynamics for both zero and second order
axes. As noted in the introduction, Chernikoff and Lemay used simple
al A*!! N * -7-I
106
disturbance inputs whose patterns could have been easily learned.
Under these circumstances, it is conceivable that highly practiced
subjects may have progressed to a pre-cognitive mode of tracking that
could be likened to automatic processing (Krendel & McRuer, 1968;
Schneider & Shiffrin, 1977; Shiffrin & Schneider, 1977; Schneider, ,
1984; Wickens, 1984a). If so, then resource demand should have
become minimal with the result that no demand effects were possible.
In some sense, this absence of resource competition between tracking
axes may have created a "noise-free" environment in which to look for
evidence of control order confusions in tracking error.
Given this perspective, Chernikoff and Lemay's heterogeneity
data can be reconciled with the present findings. Specifically, the
demand effect of the present experiment can be added to the
heterogeneity effect of the Chernikoff and Lemay study. If the
demand effect is sufficiently large compared to the heterogeneity
effect, then the latter will be masked by the former. Additional
research will be needed to evaluate this possibility.
Perception of Structure: An Alternative to Resources and Confusions
The focus of this paper has been on resource competition and
confusions in dual axis tracking. But the discussion would not be
complete without acknowledging Lintern's (in preparation) recently
proposed alternative to attention-based accounts of complex task
performance. Writing from the perspective of ecological psychology
(e.g., Gibson, 1979), he suggests that performance decrements arise
a,.
10'?
from poorly learned task structures. For example, subjects may
easily learn the pattern of a tracking disturbance function made up
of Just one sinusoid. But if a second task somehow distracts
subjects from attending to the tracking task, then they may not
discover the pattern as quickly as otherwise. As will be seen,
Lintern's hypothesis can account for certain features of the present
data but seems unable to account for the data in its entirety.
In the present study, subjects were presented with random
appearing disturbance functions so that there was no obvious pattern
.t to be discovered. But this does not mean that the task lacked
structure. Rather than residing in the disturbance function, task
structure resided in the control dynamics of each axis. That is, the
control dynamics constrained how subjects could successfully perform
the task. If subjects discovered the nature of those dynamics, thenthey could generate the appropriate kinds of control actions to
reduce tracking error; if they did not, then tracking errors would be
large.
According to this "discovery of structure" hypothesis, subjects
in the heterogeneous control conditions should have had greater
4difficulty than those in homogeneous conditions in learning thea
control dynamics appropriate to each axis. This is because subjects
can not learn the dynamics on one axis while attending to another
axis having different dynamics. But if, as in the homogeneous
conditions, the dynamics are the same on both axes, then subjects
U
108
will always learn something about the dynamics on both axes no matter
to which axis they happen to attend.
Since heterogeneous subjects appear to have attended more to the
second order rather than to the first order axis, these
considerations suggest that the first order dynamics should bave been
learned less well than the second order dynamics. One way to gauge
such learning is by examining the optimality of subject's single axis
open loop describing functions. Optimality is defined here with
respect to the response needed to make the human-plant combination
behave as a first order system. Thus, the optimal human open loop
response to a first order system is a zero order response with a gain
slope of zero dB per decade and a phase intercept of zero degrees.
Likewise, the optimal response to a second order system is a
minus-first order response with a gain slope of 20 dB per decade and
phase intercept of 90 degrees. The fact that heterogeneous and
homogeneous dynamics subjects differed with respect to the optimality
of the single task first order response but not the second order
response seems consistent with the discovery of structure hypothesis.
Whether the other major findings of the present experiment could
also be handled by the discovery of structure hypothesis is unclear,
but it seems unlikely. How, for example, would the hypothesis
explain the axis confusions associated with integrated controls or
the control stick confusions associated with separated displays?
Nevertheless, the perception of structure may be one of several
%.
I
109
important process needed to fully account for dual axis tracking
performance.
Summary
The present study had two goals. One was to examine how the
integrality of displays and controls interact with each other and
with the heterogeneity of control dynamics to shape dual axis
tracking performance. The other goal was to place this interaction
into some theoretical context that would facilitate generalization to
manual control tasks such as exist in aviation. Three major
theoretical frameworks were considered: resource theory, confusions -
theory, and Vickens' (1986c) compatibility of proximity hypothesis.
As Figure 21 suggests, resource and confusion theory together
account for the costs associated with the various experimental
manipulations while compatibility of proximity describes the
benefits. In addition, the figure identifies the particular
dependent measures in which the costs and benefits of the various
experimental manipulations were evident.
In general, the experimental results and their interpretation
are clear. First, there does not appear to be a cost to dynamics
heterogeneity per , although weak evidence for control order
confusions may have been observed in the first order axis Rather,
tracking error seems to increase primarily as a function of the
summed difficulty or resource demand of the dynamics on the two axes.
This interpetation in terms of resource demand was supported by
S
110
appropriate changes in subjects' control activity as indexed by their
open loop control gain and control velocity.
Second, while display and control integrality both led to
confusions (secondary and primary cross-coherence), those confusions
did not lead to increased tracking error nor to attenuated open loop
gain. If anything, confusions were associated with improvements in
other measures of tracking performance suggesting that different
processes underlie the different measures.
Third, separated displays led to greater tracking error,
presumably because of the visual scanning requirements involved.
While such a scanning cost was absent if heterogeneous control
dynamics were used, this absence appears to have resulted from
subject attentional allocation strategies rather than from dynamics
heterogeneity itself. Nevertheless, the resulting display by
dynamics heterogeneity interaction is empirically consistent with the
compatibility of proximity hypothesis if compatibility is understood
as an intervening variable rather than a hypothetical construct.
Yet, because the underlying allocation strategy may be specific to
the laboratory tracking task, it may be safest to assume that
integrated displays will lead to less error in most "real world"
tasks regardless of control heterogeneity.
Fourth, there appears to be a compatibility of integrality
principle in which dual axis tracking performance benefits if
displays and controls are both integrated or both separated but
, '" -", • ' ...-.- .. .... - -'' ',".""". . " .- ' .. [ " "" * " " " -" ' "
lii
suffers if one is integrated and the other is separated. This
principle may be viewed as a special case of the compatibility of
proximity. For most applications, then, the critical question may
not be whether displays or controls are integrated but whether the
configurations of the two match.
These results encourage a view that resource theory, confusions
theory, and the compatibility of proximity hypothesis each contribute
something different to an overall understanding of complex task
performance. The data show a clear dissociation between documented
confusions and most other measures of performance. Resource theory
presents a coherent account of the heterogeneity of dynamics
manipulation. Confusions theory seems able to account for the main
effects of control and display integrality. Compatibility of
proximity seems to account for the interaction between displays and
controls.
Future research may be able to extend the documentation of
confusions and compatibility effects to tasks other than dual axis
tracking. If so, and if these processes can be distinguished from
demand effects, then the prognosis for a general theory of complex
task performance may be promising.
r,
p
,?
112
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VITA
Martin Lee Fracker was born on June 17, 1953, in Seattle,
Washington. Following his graduation from Chief Sealth High School
(Seattle) in 1971, Martin attended college at LeTourneau College in
Longview, Texas, for one year and then transferred to Seattle Pacific
University in Seattle. He graduated magna cum laude from Seattle
Pacific in 1977 with a double major in Theater Arts and Psychology.
In the fall of 1977, Martin entered the Master of Science program in
Psychology at Western Washington University, Bellingham, Washington.
During the following summer, Martin entered the United States Air
Force as a reserve (active duty) second lieutenant. With the
assistance of the Air Force, Martin completed the Master of Science
degree at Western in 1981.
While working on his master's degree, Martin was assigned to the
Sheppard Technical Training Center, Sheppard Air Force Base, Texas,
where he advised the Center commander on the applications of
psychological research to training technology. As a result of his
work at Sheppard. Martin was promoted to captain, granted a Regular
commission, and awarded the Air Force Commendation Medal.
In late 1981, Martin was reassigned to the Occupational
Measurement Center, Randolph Air Force Base, Texas. As an
occupational analyst Martin conducted several studies of airmen
career fields in order to evaluate how well they were organized and
how effectively they trained their personnel. One of these studies
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131
led to a high level meeting at United States Air Force Headquarters,
Washington, D. C., at which Martin was the principal presenter. One
outcome of this meeting was a major restructuring of one of the
largest career fields in the Air Force. As a result of this and
other achievements, Martin was awarded the Meritorious Service Medal
and selected to enter the University of Illinois doctoral program in
Psychology at Air Force expense. -
Martin began his doctoral studies at the University of Illinois
in 1984 and graduated in 1987. His achievements during those three
years led to membership in the national Honor Society of Phi Kappa
Phi. In 1986, the Armstrong Aerospace Medical Research Laboratory at
Wright-Patterson Air Force Base, Ohio, issued a "by name" request for
Martin based on the recommendation of his academic advisor. In early
1987, this request was granted by the Air Force, and Martin was
transferred to the Laboratory following completion of his doctorate.
Publications
Fracker, M. L., & Wickens, C. D. (1987). Resources, confusions, and
compatibility in dual axis tracking: Displays, controls, and"'
dynamics. In E. L. Weiner (Ed.), Proceedings of the 31st annual
meeting of the Human Factors Society. Santa Monica, CA: Human
Factors Society.
Wickens, C. D., Fracker, K. L., & Webb, J. (1987). Cross modal
interference and task integration: Resources or preemption
switching? In E. L. Weiner (Ed.), Proceedings of the 31st annual
% %-%
132
meeting of the Human Factors Society. Santa Monica, CA: Homnan
Factors Society.
Wickens, C. D., Kramer, A., Barnett, B., Carswell, M., Fracker, L.,
Goett., B, & Harwood, K. (1985). Display/cognitive interface:
The effect of information integration requirements on display
formatting In C3 displays (Report No. EPL-85--2/RADC-85-l,
December). Champaign: University of Illinois, Engineering 4
Psychology Research Laboratory /Aviation Research Laboratory
Technical.
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